Question

Consider driving a car in one direction along a straight road for 10 minutes. You start from rest. During the first 1 minute, you speed up with constant acceleration until you reach 60 m/s. During the next 5 minutes, you maintain constant speed at 60 m/s. During the final 4 minutes, you have constant negative acceleration (i.e. deceleration) until you are not moving.

How far in total did you travel during the whole 10 minutes? Express your answer in units of meters.

Answer 1

Initial speed of the car = V₁ = 0 m/s

Time period of the first part = T₁ = 1 min = 1 x 60 sec = 60 sec

Speed reached at the end of first part = V₂ = 60 m/s

Constant acceleration of the car in the first part = a₁

V₂ = V₁ + a₁T₁

60 = 0 + a₁(60)

a₁ = 1 m/s²

Distance traveled by the car in the first part = D₁

V₂² = V₁² + 2a₁D₁

(60)² = (0)² + 2(1)D₁

D₁ = 1800 m

Time period of the second part = T₂ = 5 min = 5 x (60) sec = 300 sec

Distance traveled by the car in the second part = D₂

The car travels at constant speed in the second part.

D₂ = V₂T₂

D₂ = (60)(300)

D₂ = 18000 m

Time period of the third part = T₃ = 4 min = 4 x (60) sec = 240 sec

Final speed of the car = V₃ = 0 m/s

Acceleration of the car in the third part = a₃

V₃ = V₂ + a₃T₃

0 = 60 + a₃(240)

a₃ = -0.25 m/s² (Negative as it is deceleration)

Distance traveled by the car in the third part = D₃

V₃² = V₂² + 2a₃D₃

(0)² = (60)² + 2(-0.25)D₃

D₃ = 7200 m

Total distance traveled by the car = D

D = D₁ + D₂ + D₃

D = 1800 + 18000 + 7200

D = 27000 m

Total distance you traveled in the whole 10 minutes = 27000 m