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Question

A body of mass 0.40 kg moving initially with a constant speed of 10 m s-1 to the north is subject to a constant force of 8.0 N directed towards the south for 30 s. Take the instant the force is applied to be t = 0, the position of the body at that time to be x = 0, and predict its position at t = –5 s, 25 s, 100 s.

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Solution

Given: The mass of the body is 0.40kg, the initial speed of the body is 10m/s towards the north and the force acting on the body towards the south for 30s is 8.0N, the position of the body at time t=0 is x=0 and the force is applied from an instant t=0.

As the force is applied at the instant t=0 therefore, the acceleration of the body at =5s is zero.

The position of the body at t=5s can be calculated using second equation of motion.

s 1 =ut+ 1 2 a t 2 (1)

Where, u is the initial speed and a is the acceleration.

By substituting the values in the above equation, we get

s 1 =10( 5 )+ 1 2 ( 0 ) ( 5 ) 2 =50m

Thus, the position of the object at t=5s is 50m.

From Newton’s second law, the acceleration of the object after t=0s is given as,

a= F m

Where, F is the force applied and m is the mass of the object.

By substituting the values in the above expression, we get

a= 8.0 0.40 =20 m/s 2

By substituting this value in equation (1) at t=25s, we get the position of the body as,

s 2 =10( 25 )+ 1 2 ( 20 ) ( 25 ) 2 =6000m =6km

Thus, the position of the object at t=25s is 6km.

As the force is applied for 30s therefore, the acceleration works only for this time period.

The position of the body at t=30s can be calculated from equation (1).

s 3 =10×30+ 1 2 ( 20 ) ( 30 ) 2 =8700m

The velocity of the body at t=30s can be calculated as,

v=u+at

By substituting the values in the above equation, we get

v=10+( 20 )( 30 ) =590m/s

For the next 10030=70s, body moves with this uniform velocity.

The position of the body at t=100s can be calculated as,

s 4 = s 3 +v t

By substituting the values in the above equation, we get

s 4 =8700+( 590 )( 70 ) =50000m =50km

Thus, the position of the object at t=100s is 50km.


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