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Instantaneous Force and Impulse

A body is mov...

Question

A body is moving with velocity $30 m/s$ . A variable force $a N$ is applied at $t = 0 s$ on the body such that it increases it's velocity to $90 m/s$ at $t = 4 s$ in same direction. The variation of force with time is shown in graph.

If mass of body is $10 k g$ , find the value of $a$ (shown in graph)

150 N

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100 N

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50 N

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125 N

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Solution

The correct option is A $150 N$

We know
Impulse imparted by force for $(t = 0) s to (t = 4) s =$ {area under (F-t) graph from $(t = 0 s) to (t = 4 s)$ }
Also impulse imparted by force $= Δ m v$
$\Rightarrow a \times 4 = m Δ v$
$4 a = 10 \times [90 - 30]$
$4 a = 10 \times 60$
$a = 150 N$

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Q. A body of mass 10 kg is moving with a velocity of 20 m/s. A force is applied to it so that in 10 s it acquires a velocity of 40 m/s. The force applied is:

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A body is moving with velocity 30 m/s. A variable force a N is applied at t=0 s on the body such that it increases it's velocity to 90 m/s at t=4 s in same direction. The variation of force with time is shown in graph. If mass of body is 10 kg, find the value of a (shown in graph)

The correct option is A 150 N We know Impulse imparted by force for (t=0) s to (t=4) s= {area under (F-t) graph from (t=0 s) to (t=4 s)} Also impulse imparted by force =Δmv ⇒a×4=mΔv 4a=10×[90−30] 4a=10×60 a=150 N

The correct option is A $150 N$

We know
Impulse imparted by force for $(t = 0) s to (t = 4) s =$ {area under (F-t) graph from $(t = 0 s) to (t = 4 s)$ }
Also impulse imparted by force $= Δ m v$
$\Rightarrow a \times 4 = m Δ v$
$4 a = 10 \times [90 - 30]$
$4 a = 10 \times 60$
$a = 150 N$