# Velocity-time and Displacement-time graph for Ball dropped and rebounces back

When a ball is released from a height, it will accelerate on the way down due to the resultant force (weight) acting downwards. Just before the ball touches the ground, the velocity of the ball is the maximum. When it hits the ground, the speed decreases to 0 m/s instantly. When it rebounces back in the opposite direction, the initial velocity is the maximum. Assume ideal situation (no air resistance, no energy lost to sound or heat). The ball will rebounce back to its original height.

In reality, there is work done against air resistanceenergy converted to heat and sound when ball hits the ground, hence the ball will never reach its original height.

Note that in both situations, conservation of energy always applied. All energy is conserved, just that energy of the ball is converted to other forms like heat and sound.

### 7 thoughts on “Velocity-time and Displacement-time graph for Ball dropped and rebounces back”

1. Could you please help me understand why the speed-time graph has variable slope while the velocity-time graph has constant slopes? If speed is just the absolute value of velocity, shouldn’t the graph of speed-time also have straight slope like the velocity-time graph?

• Both speed-time and velocity-time graphs are similar in terms of telling you the speed (velocity) of an object at any given time. Hence both can be variable (non-uniform) slope, in which the slope represents the acceleration. The only difference is that speed is a scalar quantity (magnitude) while velocity is a vector quantity (has both magnitude and direction).

But strictly speaking, the graph should be velocity-time graph in order for the slope to represent acceleration. As acceleration is a vector quantity and acceleration is the rate of change of velocity (not speed).

In reality most object motions are never straight slope (ie uniform acceleration). In question, usually there are straight slope for calculation of acceleration.

So simply put, you can interpret both graphs in a similar way for most situations where the graph is the acceleration and the area under the graph represents the distance travelled.

Hope this helps to clarify your doubts.

Happy new year to you =)

2. Could you please help me understand why the speed-time graph has variable slope while the velocity-time graph has constant slopes? If speed is just the absolute value of velocity, shouldn’t the graph of speed-time also have straight slope like the velocity-time graph?

3. can we take the direction of velocity downward as negative acc to sign convention

• Yes. That means u take upward direction as positive. Since the ball falls downward, the graph will have a negative portion first.

4. draw a velocity-time graph for a tennis ball which is being volleyed backwards and forwards by two players close to the net. Assume that the ball travels horizontally and perpendicular to the net but that the players hit it so that it travels at a variety of speeds.

• The graph will have alternate ‘rectangles’ above and below the x-axis with various heights depends on the speed. The graph is flat if u assume no air resistance. Is it correct?