Question

Explain the velocity-tune graphs of an object:

i) Moving with zero acceleration. 

ii) Moving with constant positive acceleration. 

iii) Moving with constant negative acceleration. 

iv) Moving with non-uniform acceleration.

Answer 1

i) Object is moving with zero acceleration:

2. As the acceleration is zero, the graph will be a straight line parallel to time axis.

3. Velocity of the particle is constant as the acceleration is zero.

4. Magnitude of displacement of object from t₁ to t₂ graph.

ii) Object is moving with constant positive acceleration:

1. The velocity-time graph is linear.

2. Velocity increases with increase in time. as acceleration is positive (along the direction of velocity).

3. The area under the velocity-time graph between t₁ and t₂ gives the displacement of the object during that time interval.

4. Slope of the graph is \(\frac{\triangle\,V}{\triangle\,t}\) = positive acceleration

iii) Object is moving with constant negative acceleration:

1. The velocity-time graph is linear.

2. Velocity decreases with increase in time as acceleration is negative (opposite to the direction of velocities).

3. The area tinder the velocity-time graph between two instants of time t₁ and t₂ gives the displacement 0f the object during that time interval.

4. Slope of the graph is \(\frac{\triangle\,V}{\triangle\,t}\) negative acceleration

iv. Object is moving with non-uniform acceleration:

2. Velocity-time graph is non-linear.

3. The area under the velocity-time graph between two instants of time t₁ and t₂ gives the displacement of the object during that time interval area under the velocity-time curve =

= x(t₂) – x(t₁)

displacement of the object from t₁ to t₂.