10. A car is moving in a straight line starts from rest, accelerates uniformly at 12 m/s2 for the first 5s, then travels at uniform speed for the next 2s and finally decelerates uniformly at 4 m/s2 for the next 5s. Draw the acceleration-time graph, velocity-time graphs and determine the distance travelled by the car during given time period.
d1 = 0.5a*t^2 = 0.5*12*5^2 = 150 m.
V1 = a*t = 12 * 5 = 60 m/s.
d2 = V*t = 60m/s * 2s = 120 m.
d3 = Vo*t + 0.5a*t^2
d3 = 60*5 - 0.5*4*5^2 = 250 m.
d = d1+d2+d3 = 150+120+250 = 520 m.
To draw the acceleration-time graph, we need to break down the motion into three phases: acceleration, constant velocity, and deceleration.
Phase 1: Acceleration from rest to a constant velocity.
The car starts from rest and accelerates uniformly at 12 m/s^2 for 5 seconds. The acceleration-time graph for this phase would be a straight line with a slope of 12 m/s^2 and a duration of 5 seconds.
Phase 2: Constant velocity.
After reaching the constant velocity, the car travels at a uniform speed for 2 seconds. Since the velocity is constant, the acceleration during this phase is zero. Therefore, the acceleration-time graph for this phase would be a flat line at zero.
Phase 3: Deceleration to rest.
The car then decelerates uniformly at 4 m/s^2 for 5 seconds. The acceleration-time graph for this phase would be a straight line with a slope of -4 m/s^2 and a duration of 5 seconds.
Now let's move on to the velocity-time graph.
Phase 1: Acceleration from rest to a constant velocity.
Since the car starts from rest, the initial velocity is zero. The velocity-time graph for this phase would be a straight line with a positive slope of 12 m/s^2 and a duration of 5 seconds.
Phase 2: Constant velocity.
During this phase, the car maintains a constant velocity. Therefore, the velocity-time graph for this phase would be a horizontal line at the constant velocity for a duration of 2 seconds.
Phase 3: Deceleration to rest.
The car decelerates uniformly during this phase. To determine the final velocity, we can use the formula: final velocity = initial velocity + (acceleration * time). The initial velocity would be the constant velocity reached in phase 2. The deceleration is -4 m/s^2 and the time is 5 seconds. Once we have the final velocity, we can draw a straight line on the velocity-time graph starting from the constant velocity and ending at zero velocity.
To determine the distance traveled by the car during the given time period, we need to find the areas under the velocity-time graph.
Phase 1: The area under the velocity-time graph for this phase represents the distance traveled during acceleration. The formula to calculate this area is: area = (velocity at the end of the phase - velocity at the start of the phase) * time. Therefore, the distance traveled during this phase would be (12 m/s * 5 s) = 60 meters.
Phase 2: Since the velocity is constant, the distance traveled during this phase is given by the formula: distance = velocity * time. Therefore, the distance traveled during this phase would be (12 m/s * 2 s) = 24 meters.
Phase 3: The area under the velocity-time graph for this phase represents the distance traveled during deceleration. The final velocity is zero, and the initial velocity is the constant velocity reached in phase 2. Therefore, the distance traveled during this phase would be (12 m/s * 5 s) = 60 meters.
Adding up the distances traveled during each phase, the total distance traveled by the car during the given time period is 60 + 24 + 60 = 144 meters.