Test: Introduction to Motion in a Straight Line - ACT MCQ

The average velocity is obtained by dividing total displacement by total time taken. Instantaneous velocity is calculated at an instant and not over a period of time. Speed is distance divided by time. Velocity is said to be uniform when velocity at every instant is equal to the average velocity.

Rectilinear motion happens along a straight line. A straight line is one dimensional. Hence, rectilinear motion is one dimensional.

The hands of a clock move in a circular manner. Hence, the motion exhibited is circular motion. Moreover, it happens periodically, so it is also periodic motion. But its is not rectilinear motion.

The body moves in the state of motion. Hence it has a velocity and so kinetic energy. Kinetic energy = (1/2)mv².

The rate of change of displacement of a body is velocity. The rate of change of rate of displacement of a body, or rate of change of velocity is acceleration.

When the body is in the state of rest, there is no motion. Hence there is no kinetic energy, hence the total energy of the body is stored as its potential energy. The total energy is the sum of kinetic and potential energies.

In the physical world, no surface is frictionless. Hence whenever a body moves, the force of friction acts on it. Rest all forces act on the body only when it moves along a curve and not along a straight line.

The motion of a car on straight road is happening along a straight line. Hence the motion can be called rectilinear as rectilinear motion happens along a straight line. Rest all are non rectilinear motions.

Concept:

A. When two bodies move uniformly in opposite direction, the velocities gets added up.

B. When two bodies move uniformly in same direction, the velocities gets subtracted.

Calculation:

Given:

Let one bodies be A and B, and theor speed be V and U respectively.

As per the problem;

V_A + V_B = 6  ------(i)

V_A - V_B = 4  ------(ii)

Adding eq (i) and eq (ii)

2VA = 10

∴ VA = 5 m/s

Similarly

VA + VB = 6

5 + VB = 6

∴ VB  = 1 m/s

Concept:

For a body moving in a straight line with constant acceleration, then

• v = u + at --- (1)
• s = ut + 0.5at² --- (2)
• v² = u² + 2as --- (3)
• Where u = initial velocity, v = final velocity, a = acceleration, s = displacement, t = time

Calculation:

Given that, for first ball, height, h₁ = h and let time = t₁

And for the second ball, height, h₂ = 2h and time = t₂

Since the object is falling freely then acceleration = g

Initial velocity for both the bodies, u = 0

Then from equation 2, for first ball

h₁ = ut + 0.5gt₁² 

⇒ h = 0 + 0.5gt₁² --- (4)

For second ball,

h₂ = ut + 0.5gt₂²

⇒ 2h = 0 + 0.5gt₂² --- (5)

Dividing equation 4 by 5