Question

A particle has an initial velocity of 30 m/s due east and a constant acceleration of 10 m/s² due west. The distance covered by the particle in the one second of its motion is:
1. 10 m
2. 20 m
3. 25 m
4. 35 m

Answer 1

Correct Answer - Option 3 : 25 m

CONCEPT:

• Velocity: The rate of change of displacement of an object is velocity.
• Acceleration: The rate of change of velocity of an object is an acceleration.
• Equations of motion describe the behaviour of a physical system in terms of its motion as a function of time.
• If an object is moving with constant acceleration 'a', initial velocity 'u', the distance travelled in tth second is given by:

\(\Rightarrow s = u + {1\over 2}a (2t-1)\)

s is the distance travelled in tth second.

CALCULATION:

Given: Initial velocity of the body u = 30 m/s and acceleration of the body (a) = -10 m/s²

• Distance covered in tth second:

\(\Rightarrow s = u + {1\over 2}g (2t-1)\)

• Distance travelled in the 1st second: t = 1;

\(\Rightarrow s = 30 - {10\over 2} (2-1) = 25 m\)