Question

A force in the negative direction of an x axis is applied for 27 ms to...

A force in the negative direction of an x axis is applied for 27 ms to a 0.40 kg ball initially moving at 14 m/s in the positive
direction of the axis. The force varies in magnitude, and the impulse has magnitude 32.4 N*s.

What are the ball’s (a) speed and (b)direction of travel just after the force is applied?

What are (c) the average magnitude of the force and (d) the direction of the impulse on the ball?

here,

time , t = 27 ms = 0.027 s

mass , m = 0.4 kg

intial speed , u = 14 m/s

magnitude of impulse , |I| = 32.4 N.s

let the final speed be v

as force is acting in opposite direction

(u - v ) * m = |I|

( 14 - v) * 0.4 = 32.4

solving for v

v = - 67 m/s

the final speed is 67 m/s

b)

the direction of travel after the force is applied is to the negative x-direction

c)

the average magnitude of force , |F| = I| /t

|F| = 32.4 /0.027 N = 1200 N

d)

the direction of impulse is to the negative -x direction

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