Question

An electric vehicle starts from rest and accelerates at a rate of 1.8 m/s² in a straight line until it reaches a speed of 18 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?

Answer 1

a)

During acceleration :

v_o = initial velocity = 0 m/s

a = acceleration = 1.8 m/s²

v = final velocity = 18 m/s

t = time taken

Using the equation

v = v_o + a t

18 = 0 + (1.8) t

t = 10 sec

During retardation :

v'_o = initial velocity = 18 m/s

a' = acceleration = - 1.4 m/s²

v' = final velocity = 0 m/s

t' = time taken

Using the equation

v' = v'_o + a' t'

0 = 18 + (- 1.4) t'

t' = 12.86  sec

T = Total time = t + t' = 10 + 12.86 = 22.86 sec

b)

During acceleration :

v_o = initial velocity = 0 m/s

a = acceleration = 1.8 m/s²

v = final velocity = 18 m/s

d = distance traveled  

Using the equation

v² = v²_o + 2 a d

18² = 0² + 2 (1.8) d

d = 90 m

During retardation :

v'_o = initial velocity = 18 m/s

a' = acceleration = - 1.4 m/s²

v' = final velocity = 0 m/s

d' = distance traveled

Using the equation

v'² = v'²_o + 2 a' d'

0² = 18² + 2 (- 1.4) d'

d' = 115.71 m

D = Total distance traveled = d + d' = 90 + 115.7 = 205.7 m