Asled and rider, gliding over horizontal, frictionless ice at 4.3 m/s , have a combined mass of 74 kg . the sled then slides over a rough spot in the ice, slowing down to 2.9 m/s . part a what impulse was delivered to the sled by the friction force from the rough spot?

The impulse of a force is defined as

where F is the intensity of the force and  the time of application of this force.

We can rewrite the previous relationship by using Newton's second law:

substituting, the equation for the impulse becomes


But the acceleration is the variation of the velocity in the time interval:

so we can rewrite I as


the combined mass of sled and rider is m=74 kg, while the variation of velocity is 

and so we can calculate the impulse of the friction force:

where the negative sign means the friction force acts against the motion, to decelerate the system.

The answer would be a