Question

3. A 1500 kg car accelerates from 55.0 km/h to 90.0 km/h. Calculate the impulse experienced by the
car.

Answer 1

Formula Applied :

Impulse is defined as product of force and time .

$\to \sf J=F \Delta t$

$\to \sf J=ma\Delta t\\\\\to \sf J=m\Delta v\ \; \bigstar$

Solution :

Mass , m = 1500 kg

Initial velocity , u = 54 km/h = 15 m/s

Final velocity , v = 90 km/h = 25 m/s

$:\implies \sf J=m\Delta v$

$:\implies \sf J=(1500)(v-u)$

$:\implies \sf J=(1500)(25-15)$

$:\implies \sf J=(1500)(10)$

$:\implies \sf J=15,000\ Ns\ \; \bigstar$

So , Impulse experienced by the car is 15,000 N-s .

More Info :

SI unit of Impulse :

1 . N-s

2. Kg.m/s

Answer 2

Given :

• Mass of the object = 1500 kg

• Initial velocity (u) = 55 km/h

• Final Velocity (v) = 90 km/h

To Find :

The Impulse experienced by the car.

Solution :

First let us deduce the actual formula for the Impulse or impulsive force.

We know that :

$\underline{\boxed{\bf{Impulse = Force \times time}}}$

Now by solving it , we get :

$:\implies \bf{Impulse = F \times t}$

$:\implies \bf{Impulse = m \times a \times t}\:\:[\because Force = ma]$

$:\implies \bf{Impulse = m \times \dfrac{v - u}{t} \times t}\:\:[\because a = \dfrac{v - u}{t}]$

$:\implies \bf{Impulse = m \times \dfrac{v - u}{\not{t}} \times \not{t}}$

$:\implies \bf{Impulse = m \times (v - u)}$

$:\implies \bf{Impulse = mv - mu}$

Hence, the formula for impulse is (mv - mu).

⠀⠀⠀⠀⠀⠀⠀To Find the impulsive force :

We know that the Standard unit of impulse is kg m/s or N s.

So First let us convert the initial and final Velocity into m/s from km/h.

To convert the unit in m/s , multiply the velocity by 5/18.

So we get :

• v = 90 km/h

= 90 × 5/18

= 5 × 5

= 25 m/s

• u = 55 km/h

= 55 × 5/18

= 275/18

= 15.28 m/s (Approx.)

= 15 m/s

Hence, the initial velocity in m/s is 15 m/s and the final Velocity in m/s is 25 m/s.

Now , by using the above formula and substituting the values in it, we get :

$:\implies \bf{Impulse = mv - mu}$

$:\implies \bf{Impulse = (1500 \times 25) - (1500 \times 15)}$

$:\implies \bf{Impulse = 37500 - 22500}$

$:\implies \bf{Impulse = 15000}$

$\therefore \bf{Impulse = 15000\:kg ms^{-1}}$

Hence, the Impulse experienced by the car is 15000 N s.