Question

A car starts from rest and has an acceleration a = underroot t. A truck is moving with a uniform velocity of
4 m/s. At what distance will the car overtake the truck? (at t=0 both start their motion in the same
direction from the same position)
(A) 4(15)2/3 m (B) 4(4)2/3 m (C) 4(15)173 m (D) 4 m​

Answer 1

Answer:

4× 15^(2/3) ____option A

Explanation:

For overtaking both should cover equal distance x in equal time t

Car:

dv/dt = √t

dv = √t dt

v = (2/3) × t^(3/2) = dx/dt

x = (4/15) × t^(5/2) ------eqn 1

Truck

4t = x. _--------eqn 2

Solving eqn 1 and 2

x = x^(5/2) /{4^(3/2)×15}

120 = x^(3/2)

x = 120^(2/3) = 4× 15^(2/3)

t= x/4 (from eqn 1)

= 15^(2/3)