Question

The acceleration-time graph of a block of mass 4 kg moving along x-axis is as shown in the figure. If the initial velocity of block is 2 m/s, then the power delivered to the block at t = 4 s will be

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Answer 1

Answer:

From the graph, slope =

1

−2

=−2 for t>1

∴ a(t)=(−2)(t−2) ⟹a(t)=4−2t for t>2 s

Magnitude of acceleration ∣a(t)∣=2t−4 for t>2 s

Area under the a-t graph gives the change in velocity of the particle during that period.

∴ ΔV=2×1+

2

1

×1×2−

2

1

×(2t−4)×(t−2)

⟹ ΔV=3−(t−2)

2

Let the particle acquires its initial velocity again after time t

1

i.e ΔV=0 at t=t

1

∴ 0=3−(t

1

−2)

2

⟹t

1

=2+

3

s and t

1

=2−

3

s (Not possible)

Thus the particle acquires its initial velocity again at t=2+

3

s

solution

Answer 2

Answer:

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