Question

In: Physics

An electric vehicle starts from rest and accelerates at a rate of 2.4 m/s2 in a...

An electric vehicle starts from rest and accelerates at a rate of 2.4 m/s² in a straight line until it reaches a speed of 27 m/s. The vehicle then slows at a constant rate of 1.4 m/s² until it stops. (a) How much time elapses from start to stop? (b) How far does the vehicle move from start to stop?

Expert Solution

Initial speed of the vehicle = V₀ = 0 m/s (At rest)

Maximum speed the vehicle reaches = V₁ = 27 m/s

Acceleration of the vehicle while speeding up = a₁ = 2.4 m/s²

Time period the vehicle speeds up for = T₁

V₁ = V₀ + a₁T₁

27 = 0 + (2.4)T₁

T₁ = 11.25 sec

Distance the vehicle travels while speeding up = D₁

D₁ = V₀T₁ + a₁T₁²/2

D₁ = (0)(11.25) + (2.4)(11.25)²/2

D₁ = 151.88 m

Final speed of the vehicle = V₂ = 0 m/s (Comes to a stop)

Acceleration of the vehicle while slowing down = a₂ = -1.4 m/s² (Negative as it is deceleration)

Time period taken for the vehicle to come to a stop = T₂

V₂ = V₁ + a₂T₂

0 = 27 + (-1.4)T₂

T₂ = 19.29 sec

Distance the vehicle travels while slowing down = D₂

V₂² = V₁² + 2a₂D₂

(0)² = (27)² + 2(-1.4)D₂

D₂ = 260.36 m

Total time elapsed from start to stop = T

T = T₁ + T₂

T = 11.25 + 19.29

T = 30.54 sec

Total distance traveled by the vehicle = D

D = D₁ + D₂

D = 151.88 + 260.36

D = 412.24 m

a) Total time elapsed from start to stop = 30.54 sec

b) Total distance traveled by the vehicle = 412.24 m

genius_generous answered 1 year ago

An electric vehicle starts from rest and accelerates at a rate of 2.1 m/s2 in a...

An electric vehicle starts from rest and accelerates at a rate of 2.1 m/s2 in a straight line until it reaches a speed of 17 m/s. The vehicle then slows at a constant rate of 1.1 m/s2 until it stops. (a) How much time elapses from start to stop? (b) How far does the vehicle move from start to stop? solve both a b show units

A car starts from rest at a stop sign. It accelerates at 5.56 m/s2 for 6.56...

A car starts from rest at a stop sign. It accelerates at 5.56 m/s2 for 6.56 seconds, coasts for 3.6 s, and then slows down at a rate of 3.93 m/s2 for the next stop sign. How far apart are the stop signs?

A train starts from rest and accelerates uniformly with a = 2 m/s2 until it has...

A train starts from rest and accelerates uniformly with a = 2 m/s2 until it has traveled 1 km. The train then moves at a constant velocity of 20 m/s for one hour. The train then slows down uniformly at 0.05 m/s2, until it stops. Calculate: The maximum speed of the train The total distance traveled by train.

An object starts from rest and accelerates at a rate of 2 rad/s2 until it reaches...

An object starts from rest and accelerates at a rate of 2 rad/s2 until it reaches an angular speed of 23 rad/s. The object then accelerates at a constant rate of a rad/s2 until it stops. If the angular displacement is 193 rad, what is the angular acceleration a (in rad/s2)?

a). A prototype car starts from rest and accelerates at a constant rate to 30 m/s...

a). A prototype car starts from rest and accelerates at a constant rate to 30 m/s in 5.6 seconds. How much distance did the car travel during the 5.6-second accelerated motion? b). A car was parked on the side of a hillside road at the top of a hill. Unbeknown to the owner, its parking brake failed and tremors from nearby construction set it in motion with negligible initial speed down the hill. Assume the acceleration was constant down the...

a). A prototype car starts from rest and accelerates at a constant rate to 60 m/s...

a). A prototype car starts from rest and accelerates at a constant rate to 60 m/s in 4.1 seconds. How much distance did the car travel during the 4.1-second accelerated motion? b). A single-engine air plain starts its engine at one end of the runway. It accelerates at a constant rate and takes off at 36 m/s after 29 seconds on the runway, just as it is running out of runway. How long is the runway? c). An object is...

A flywheel with a radius of 0.390 m starts from rest and accelerates with a constant...

A flywheel with a radius of 0.390 m starts from rest and accelerates with a constant angular acceleration of 0.670 rad/s2. Compute the magnitude of the tangential acceleration, the radial acceleration, and the resultant acceleration of a point on its rim at the start. Compute the magnitude of the tangential acceleration, the radial acceleration, and the resultant acceleration of a point on its rim after it has turned through 60.0 ∘. Compute the magnitude of the tangential acceleration, the radial...

A flywheel with a radius of 0.400 m starts from rest and accelerates with a constant...

A flywheel with a radius of 0.400 m starts from rest and accelerates with a constant angular acceleration of 0.640 rad/s2. A. Compute the magnitude of the tangential acceleration, the radial acceleration, and the resultant acceleration of a point on its rim at the start. Express your answers in meters per second squared separated by commas. B. Compute the magnitude of the tangential acceleration, the radial acceleration, and the resultant acceleration of a point on its rim after it has...

a car starts from rest and accelerates at 3m/s2 until it hits 30m/s and then coasts...

a car starts from rest and accelerates at 3m/s2 until it hits 30m/s and then coasts at this constant velocity. How much time does it take to complete a 450m trip? can someone help please

A subway train starts from rest at a station and accelerates at a rate of 2.00...

A subway train starts from rest at a station and accelerates at a rate of 2.00 m/s2 for 14.0 s. It runs at constant speed for 66.0 s and slows down at a rate of 4.00 m/s2 until it stops at the next station. Find the total distance covered.