A car starts from rest and has an acceleration a=√t . A truck is moving with uniform velocity of 4 m/s . At what distance will be the car overtake the truck ? (At t=0 both start their motion in the same direction from same position)?

Question

Answer

Problem

A car starts from rest and has an acceleration a=√t. A truck is moving with uniform velocity of 4 m/s. At what distance will be the car overtake the truck ? (At t=0 both start their motion in the same direction from same position)?

Solution

Let's first find the equation of motion for the car:

Initial velocity of the car, u = 0

Acceleration of the car, a = √t

Using the equation of motion, s = ut + 1/2 at^2, we get:

s = 1/2 (√t) t^2 = 1/2 t^(5/2)

Now, let's find the time it takes for the car to overtake the truck:

Let the time taken by the car to overtake the truck be t_o

Distance covered by the truck in time t_o, S_t = 4t_o

Distance covered by the car in time t_o, S_c = 1/2 t_o^(5/2)

At the point of overtaking, both the truck and the car will cover the same distance:

S_t = S_c

4t_o = 1/2 t_o^(5/2)

Solving for t_o, we get t_o = 16/25 s

Finally, let's find the distance at which the car overtakes the truck:

Using the equation of motion for the car, s = 1/2 t^(5/2), we get:

s = 1/2 (16/25)^(5/2) = 0.8 m

Therefore, the car will overtake the truck at a distance of 0.8 m.

Answer

16

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