Question

The distance-time graph for uniformly accelerated motion is:
1. hyperbola
2. parabola
3. circle
4. straight line

Answer 1

Correct Answer - Option 2 : parabola

The correct answer is option 2) i.e. parabola

CONCEPT:

• Acceleration is defined as the rate of change of velocity.​
  • The slope of the velocity-time graph gives acceleration.
• Velocity is the rate of change of distance for straight-line motion.
  • ​The slope of the distance-time graph gives velocity.

​EXPLANATION:

• ​For uniform acceleration, the rate of change of velocity must be constant, i.e. the slope of the velocity-time graph will be constant.
• At uniform acceleration, the velocity is increasing constantly.
• For the velocity to increase, the slope of the distance-time graph must be increasing with time. Velocity is increasing when the distance-time graph is a straight line or exponentially increasing curve.
• But if the distance-time graph is a straight line, the slope will be a constant i.e. velocity increases constantly with time. Hence, the acceleration will be zero.

​Distance (S) = ut + (1/2)at²

Where u is initial velocity, t is time and a is the uniform acceleration

​Hence, the distance-time graph must be an increasing curve like a parabola for a continuous increase in velocity that produces uniform acceleration.