A car whose speed is 20 m/s passes a stationary motorcycle which immediately gives chase with a constant acceleration of 2.4 m/s2 .

Question

how far will the motorcycle travel before catching the car. I know the answer is 333 but I need help getting there. thanks 😊

Answer 1

v = speed of car =  20 m/s

 

a = acceleration of motorcycle = 2.4 m/s²

 

They are both at distance x from the starting point of the motorcycle, where the car initially passes the stationary motorcycle.

 

Car:

 

x = vt

 

Motorcycle:

 

x = (1/2)at² + ut + x₀

 

u = initial speed of motorcycle = 0 (started from rest)

x₀ = 0

 

Then

 

x = (1/2)at² 

 

Put it all together:

 

vt = (1/2)at²

 

v = at/2

 

t = 2v/a

 

x = vt = v(2v/a) = 2v²/a = 2(20 m/s)² / (2.4 m/s²) ≅ 333.3 m