A car is moving with the accelaration 2 m/`s^(2)` from rest. Find the distance traveled by the car in 10th second.

Explanation

The situation is shown in the figure. Suppose the mass of the bob is m and the string makes an angle `theta` with the vertical. We shall work from the car frame. This frame is non-inertial as it has an acceleration `veca_0` with respect to an inertial frame (the road). Hence, if we use Newton's second law we shall have to include pseudo force.

Take the bob as the system.
The force are:
a. T along the string, by the string
b. mg downward, by the earth
c. `ma_0` towards left (pseudo force).
The free body diagram is shown in figure. As the bob is at rest (remember we are discussing the motion with respect to the car) the force in a, b, c should add to zero. Take X-axis along the forward horizontal direction and Y-axis along the upward vertical direction. The components of the along the X-axis is given
`T sin theta -ma_0=0 or, T sin theta = ma_0` ...........i
And the components along the Y-axis give
`Tcos theta -mg=0 or, T cos theta=mg` ..........ii.
Dividing i. by ii `tantheta =a_0/g`
Thus, the string makes an angle `tan^-1(a_0/g)` with the vertical.