. Obtain a relation for the distance travelled by an object moving with a uniform acceleration in the interval between the 4th and 5th seconds.

Soln:

a = dv/dt

Assume that air resistance is nil.

We can directly contain it by using Newton’s equations of motion or from the below-mentioned method: Thus, the area under the v-t curve and the x-axis where the slope of the curve is the instantaneous acceleration.

In this case, acceleration g is constant, and due to the free-fall condition, the initial velocity is zero. Therefore the v-t curve is a straight line with a slope equal to g equal to 9.81 m/s passing through the origin.

On dividing the total area under the curve into the interval of unit seconds, then we initially obtain a triangle followed by trapeziums of increasing height.

The ratio of the area of the first triangle to the second triangle to the third triangle is equal to the ratio of displacement

in the first, second and third second. We get ratio equal to 1:3:5:7:9… and so on. For the 4th & 5th second, it is 7:9.