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 and deduce total speed and average speed
To draw the velocity-time graph, we can break down the motion of the vehicle into four parts: acceleration, constant speed, and deceleration.
1. Acceleration for the first 10s:
During this time, the velocity of the vehicle increases at a rate of 1.5m/s^2. Therefore, the velocity-time graph will show a straight line with a slope of 1.5m/s^2 for the first 10s.
2. Acceleration for the next 20s:
After the first 10s, the acceleration continues at a rate of 0.5m/s^2. This will result in a shallower slope on the velocity-time graph for the next 20s.
3. Constant speed for 90s:
After accelerating for a total of 30s, the vehicle maintains a constant speed. This will be represented by a horizontal line on the velocity-time graph for 90s.
4. Deceleration for the last 30s:
In the final 30s, the vehicle decelerates. The velocity-time graph will show a negative slope for these 30s.
The total speed of the vehicle can be calculated by finding the area under the velocity-time graph. This can be done by calculating the area of each section of the graph and summing them up.
The average speed of the vehicle can be calculated by dividing the total distance traveled by the total time taken.
I am unable to draw the graph visually, but I hope this explanation helps!