Question

1 point) A truck starts from rest and accelerates at 1?/?². 6 s later, a car accelerates from rest at the same starting point with an acceleration of 2.7?/?².

a) Where and when does the car catch the truck?
1. ?m from the starting point
2. at ? seconds from the moment the truck started to accelerate.

b) What are their velocities when they meet?
The truck :  m/s
The car :  m/s

Answer 1

Initial velocity of Truck,V_iT=0

Initial velocity of car,V_ic=0

Acceleration of truck,a_T=1 m/s²

Acceleration of car,a_c=2.7 m/s²

Let they meets at distance x from starting point.

So

For truck

x=(1/2)a_T(t-6)² ............................(1)

and for car

x=(1/2)a_c(t)² .............................(2)

From (1) and (2)

(1/2)a_T(t-6)² =(1/2)a_c(t)²

or

a_T(t-6)² =a_c(t)²

using a_T= 1 m/s² and a_c=2.7 m/s²

1.7t² +12 t -36=0

on solving

t=2.27 sec

X=(1/2)a_c(t)²=(1/2)2.72.27²=6.96 m

Part a.

1. 6.96 m

2. 2.27 sec

Part b.

Velocity of truck when they meet is

V_T=(2a_TX)^1/2=(216.96)^1/2=3.73 m/s

Velocity of car when they meet is

V_c=(2a_cX)^1/2=(22.76.96)^1/2= 6.13 m/s