Application of equation of motion — lesson. Science CBSE, Class 9.

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Let us see few examples to understand the application of the three equations of motion.

1. Practical problem using the first equation of motion:

A car cruise down an expressway at 22 \(m/s\). Engineers are designing an off-ramp in an interchange with a deceleration of −3 \(m/s²\) that lasts 3 \(s\). Then, what would be the velocity of cars at the end of the off-ramp?

Important!

A ramp, also known as an inclined plane, is a flat supporting surface tilted at an angle with one end angle is higher. It is mostly used as an aid for raising or lowering a road.

Given:

Initial velocity of car, \(u =\) 22 \(m/s\)

Acceleration of the car, \(a =\) −3 \(m/s²\)

Time, \(t =\) 3 \(s\)

To find the final velocity of the car, we can use the first equation of motion,

v = u + at

Substituting the known values,

\begin{array}{l} v = 22 m / s + (-3 m / s^{2} \times 3 s) \\ v = 22 -9 \\ v = 13 m / s \end{array}

Therefore, the car has a velocity of 13 \(m/s\) at the end of the off-ramp.

2. Practical problem using the second equation of motion:

Consider a cheetah starts from rest and accelerate uniformly at 5 \(m/s²\) for 250 \(m\). Find out the time it takes to cover this distance.

Given:

Since it starts from the rest, the initial velocity of cheetah, \(u = 0\) \(m/s\)

Acceleration of the cheetah, \(a =\) 5 \(m/s²\)

Displacement, \(s =\) 250 \(m\)

To find the time to cover this distance, we can use the second equation of motion,

s = ut + \frac{1}{2} a t^{2}

Since the displacement is given and we do not have the velocity of the cheetah, we cannot use the first equation of motion.

Substituting the known values,

\begin{array}{l} s = ut + \frac{1}{2} at \\ 250 = 0 \times t + (\frac{1}{2} \times 5 \times t^{2}) \\ 250 = \frac{1}{2} \times 5 \times t^{2} \\ 250 \times 2 = 5 \times t^{2} \\ 500 = 5 \times t^{2} \\ t^{2} = \frac{500}{5} \\ t^{2} = 100 \\ t = 10 seconds \end{array}

Therefore, cheetah will cover 250 \(m\) in 10 \(s\) if it accelerates uniformly at 5 \(m/s²\).

3. Practical problem using the third equation of motion:

A 10 car metro train is at rest in a station. It reaches its cruising speed after accelerating at 3 \(m/s²\) for a distance equivalent to the length of the station 150 \(m\). It then travels at a constant speed towards the next station 20 blocks away for (\(1325\ m\)). In such a case, determine the train's cruising velocity.