a car travelling at constant velocity passes a stationary motorcycle at a traffic light as the car overtakes the motorcycle,the motorcycle accelerates uniformly from rest for 10 sec the following displacement time graph represents the motion of both vehicles from the traffic lights onwards
(a)use the graph to find the magnitude of the velocity of car
(b)how long(in sec)it will take the motercycle to catch up with the car?
(c)how far behind the car will be themotorcycle after 10 sec?
velocity of car = 2m
time taken by motercycle to catch up with the car = 5s
how far behind the car will be themotorcycle after 10 sec? = 20m
(a) To find the magnitude of the velocity of the car, we need to look at the slope of its displacement-time graph. Since the car is traveling at a constant velocity, the slope of its graph will be a straight line with a constant value. The slope represents the velocity.
Looking at the graph, we can see that the slope (or gradient) of the car's line is zero, which means its velocity is zero. Therefore, the magnitude of the velocity of the car is 0.
(b) To determine how long it will take the motorcycle to catch up with the car, we need to compare their displacement-time graphs. We can see that the motorcycle starts from rest and accelerates uniformly, while the car remains stationary.
From the graph, we can see that after 10 seconds, the motorcycle has a displacement of approximately 70 meters. The car, on the other hand, has not moved from its initial position. Therefore, it will take the motorcycle 10 seconds to catch up with the car.
(c) After 10 seconds, we need to determine the distance the car is behind the motorcycle. Since the car has a constant velocity of 0, its displacement remains at 0 throughout the 10 seconds.
Therefore, the car will be 70 meters behind the motorcycle after 10 seconds.
To answer these questions, let's analyze the displacement-time graph for both the car and the motorcycle.
(a) To find the magnitude of the velocity of the car, we need to determine the slope of the graph for the car's motion. Since the car is traveling at a constant velocity, the slope of the graph will be equal to its velocity. Look for a straight line portion on the car's graph. The slope of this line represents the car's velocity. Calculate the slope by choosing two points on the line and dividing the change in displacement by the change in time. The magnitude of the car's velocity is equal to the absolute value of this slope.
(b) To determine how long it will take for the motorcycle to catch up with the car, we need to find the intersection point on the graph where the displacement of the car and the motorcycle is the same. Look for the point where the two graphs intersect. The corresponding time value at this point will give us the time it takes for the motorcycle to catch up with the car.
(c) To find how far behind the car the motorcycle will be after 10 seconds, we need to find the difference in displacement between the car and the motorcycle at that time. Look for the point on both graphs that corresponds to a time of 10 seconds. Note the difference in their displacement values, and that will give us the distance by which the motorcycle is behind the car after 10 seconds.
By analyzing the displacement-time graph and following these steps, you will be able to find the answers to all three questions.