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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

Solutions

Expert Solution

Given : a= 2.1 m/s² , a' = -1.1 m/s² , v= 17 m/s

Solution :

(a) Total time elapses from start to stop

Using equation of motion to find time required to reach velocity 17 m/s :

v = v₀+at₁

17 m/s = 0 +(2.1m/s²)t₁

t₁ = 17/2.1 = 8.1 s

Using equation of motion to find time requured to stop from 17 m/s velocity :

v = v₀ +a't₂

0 = (17m/s)+ (-1.1 m/s²)t₂

t₂ = 17/1.1 = 15.4 s

Total time elapses from start to stop is given by: t = t₁ + t₂

i.e. t = 8.1 s + 15.4 s = 23.5 s

Answer : 23.5 s

(b) Total distance travelled by vehicle from start to stop

Using equation of motion to find the distance traveled to reach velocity 17 m/s :

v² = v₀²+2ad₁

d₁ = (v²-v₀²)/2a

= [(17)²-0]/2(2.1)

= 68.8 m

Using equation of motion to find the distance traveled to stop from velcoti 17 m/s

v² = v₀²+2a'd₂

d₂ = (v²-v₀²)/2a'

= [(0)-(17)²]/2(-1.1)

= 131.4 m

Total distance traveled from start to stop is given by:

d = d₁ + d₂

= 68.8 m + 131.4 m

= 200.2 m

Answer : 200.2 m

genius_generous answered 3 months ago

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