Question

a car and a truck start from rest at the same instant with the car initially 50m behind the truck. The truck has a constant acceleration of 2m/s^2 and the car has a constant acceleration of 3m/s^2.

The car overtakes the truck after how many seconds?
At what speed is the car moving when it overtakes the truck?
What is the speed of the truck when its overtaken by the car?
How far has the truck traveled in meters when the car overtakes it?

Answer 1

1)
Car -
S = 50 (50m to travel to reach truck since truck is moving away at a constant acceleration)

u = o
a = 3
t = ?

S = ut + 0.5*a*t^2
50 = 0 + 0.5(3)t^2
t = sqr(100/3) = 5.77s

2)
S = 50
u = o
v = ?
a = 3
t = 5.77

v = u + at
v = 0 + 3*5.77
v = 17.3 m/s

3)

S = -
u = o
v = ?
a = 2
t = 5.77

v = u + at
v = 0 + 2*5.77
v = 11.5 m/s

4)

S = ?
u = o
v = 11.5
a = 2
t = 5.77

S = ut + 0.5at^2
S = 0 + 0.5(2)(5.77^2)
S = 33.3 m