**a) The impulse is 76.5 Ns**

**b) The average force is 546.4 N**

**c) The final speed is 31.5 m/s**

**Explanation:**

a)

The impulse exerted on an object is defined as

where

F is the magnitude of the force exerted on the object

is the time interval during which the force is applied

If we consider a graph of the force applied vs time, it follows that the impulse exerted is equal to the area under the graph.

Therefore, in this problem, we can calculate the impulse by computing the area under the graph. We have a trapezium, whose bases are

and whose height is

Therefore, the area (and the impulse) is

b)

In this problem, the force applied is not constant. However, we can rewrite the impulse also as

where

is the average force exerted during the whole time

In this problem we have

J = 76.5 Ns is the impulse (calculated in part a)

is the time interval

Solving for the average force, we find

c)

According to the impulse theorem, the impulse exerted on an object is equal to the change in momentum of the object:

where

m is the mass of the object

v is the final velocity

u is the initial velocity

In this problem, we have

J = 76.5 Ns

m = 3.0 kg is the mass

u = 6.0 m/s is the initial velocity

Solving for v, we find the final velocity (and speed):

Learn more about** impulse and momentum:**

brainly.com/question/9484203

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