Question

# 1 point) A truck starts from rest and accelerates at 1?/?2. 6 s later, a car...

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

Initial velocity of Truck,ViT=0

Initial velocity of car,Vic=0

Acceleration of truck,aT=1 m/s2

Acceleration of car,ac=2.7 m/s2

Let they meets at distance x from starting point.

So

For truck

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

and for car

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

From (1) and (2)

(1/2)aT(t-6)2 =(1/2)ac(t)2

or

aT(t-6)2 =ac(t)2

using aT= 1 m/s2 and ac=2.7 m/s2

1.7t2 +12 t -36=0

on solving

t=2.27 sec

X=(1/2)ac(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

VT=(2aTX)1/2=(216.96)1/2=3.73 m/s

Velocity of car when they meet is

Vc=(2acX)1/2=(22.76.96)1/2= 6.13 m/s