A vihecle moves from rest with a uniform acceleration of 1.5m/s2 for the first 10s and continues accelerating at 0.5m/s2 for further 20s. It continues in that speed for 90s and finally takes 30s to decelerate. Draw a velocity-time graph
To draw the velocity-time graph for the given scenario, we need to break down the motion of the vehicle into different intervals based on the acceleration or deceleration.
1. Initial acceleration at 1.5m/s^2 for 10s:
During this interval, the velocity of the vehicle increases at a uniform rate. The final velocity at the end of this interval can be calculated using the equation:
v = u + at
where v is the final velocity, u is the initial velocity (which is 0 m/s in this case), a is the acceleration (1.5m/s^2), and t is the time (10s).
v = 0 + 1.5*10 = 15 m/s
2. Acceleration at 0.5m/s^2 for 20s:
During this interval, the velocity of the vehicle continues to increase at a lesser rate compared to the initial acceleration. The final velocity at the end of this interval can be calculated using the same equation as above:
v = u + at
where u is the velocity at the end of the first interval (15 m/s), a is the acceleration (0.5m/s^2), and t is the time (20s).
v = 15 + 0.5*20 = 15 + 10 = 25 m/s
3. Constant speed for 90s:
During this interval, the velocity of the vehicle remains constant at 25 m/s.
4. Deceleration for 30s:
During this interval, the velocity of the vehicle decreases at a uniform rate. The final velocity at the end of this interval can be calculated using the same equation as above, with a negative acceleration value (-a):
v = u + at
where u is the velocity at the end of the third interval (25 m/s), a is the deceleration (-0.5m/s^2), and t is the time (30s).
v = 25 - 0.5*30 = 25 - 15 = 10 m/s
Based on these calculations, the velocity-time graph will have the following shape:
[Velocity-time graph description:
- The graph starts at 0 m/s and shows a straight line with a positive slope representing the acceleration at 1.5 m/s^2 for the first 10 seconds.
- It then transitions smoothly into a line with a lesser positive slope representing the acceleration at 0.5 m/s^2 for the next 20 seconds.
- After that, there is a horizontal line indicating constant velocity at 25 m/s for 90 seconds.
- Finally, there is a straight line with a negative slope showing the deceleration at 0.5 m/s^2 for the last 30 seconds until the velocity reaches 10 m/s.
- The velocity-time graph ends at 10 m/s.]