Question

Figure below shows the position-time graph of a particle of mass 4kg. What is the (a) force on the particle for t < 0, t > 4 s, 0 < t < 4 s (b) impulse at t = 0 and t = 4s.(Consider one dimensional motion only).

Answer 1

Hii mate,

● (a) Force-
1. For t < 0
Here, the displacement of the particle in this time interval is zero. Hence, the force acting on the particle is zero.

2. For t > 4 s
Here, the particle is at rest at a distance of
3 m from the origin. Hence, no force is acting on the particle.

3. For 0 < t < 4
Here, graph have constant slope indicating constant speed. Hence, the acceleration produced in the particle is zero. Therefore, the force acting on the particle is zero.

● (b) Impulse-
Impulse = Change in momentum
= mv – mu

1. At t = 0 s
m = 4 kg
u = 0
v = 3/4 m/s
∴ Impulse = 4(3/4–0) = 3 kgm/s

2. At t = 4 s
m = 4 kg
u = 3/4 m/s
v = 0
∴ Impulse = 4(0–3/4) = -3 kgm/s.

Hope this is useful...

Answer 2

Hey mate!!

Find the answer below

For t < 0 and t > 4 s, the position of the particle is not changing i.e. the particle is at rest. So no force is acting on the particle at these intervals.

For 0< t < 4 s, the positions of the particle is continuously changing. As the position-time graph is a straight line, the motion of the particle is uniform, so acceleration, a=0. Hence no force acts on the particle during this interval also 0.

Impulse = Change in momentum

= mv – mu

1. At t = 0 s

m = 4 kg

u = 0

v = 3/4 m/s

∴ Impulse = 4(3/4–0) = 3 kgm/s

2. At t = 4 s

m = 4 kg

u = 3/4 m/s

v = 0

∴ Impulse = 4(0–3/4) = -3 kgm/s.

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