A force acting on the body of mass 10kg changes its velocity from 30 miles/hr to 45 miles/hr find the impulse of the force...

To find the impulse of a force, you need to use the formula for impulse. Impulse (J) is given by the product of the force (F) acting on an object and the time interval (Δt) over which the force is applied. Mathematically, it can be expressed as:

J = F * Δt

Given that the mass of the object is 10 kg, we need to first convert the velocities from miles per hour to meters per second, as the SI unit system (which we commonly use in physics) is based on meters and seconds.

1 mile = 1.60934 kilometers
1 kilometer = 1000 meters
1 hour = 3600 seconds

So, to convert miles per hour to meters per second, we can use the following conversions:

30 miles/hr * 1.60934 km/mile * 1000 m/km / 3600 s/hr = 13.4111 m/s (initial velocity)

45 miles/hr * 1.60934 km/mile * 1000 m/km / 3600 s/hr = 20.1167 m/s (final velocity)

The change in velocity (Δv) is then calculated by subtracting the initial velocity from the final velocity:

Δv = final velocity - initial velocity
= 20.1167 m/s - 13.4111 m/s
= 6.7056 m/s

Now, we can find the impulse by multiplying the change in velocity by the mass of the body:

J = F * Δt

Since the force is not given, we cannot directly determine the impulse without additional information.

However, if the force acting on the body is constant, we can use Newton's second law, which states that force (F) is equal to the mass (m) times the acceleration (a). Rearranging the equation, we have:

F = m * a

Since Δv = a * Δt, we can substitute this into the impulse formula:

J = F * Δt
= (m * a) * Δt
= m * (a * Δt)
= m * Δv

Substituting the given values:

J = (10 kg) * (6.7056 m/s)
= 67.056 kg·m/s

Therefore, the impulse of the force is 67.056 kg·m/s.