A vehicle accelerates uniformly form rest, from West to East, to a velocity of 60 m/s in 40 s. (a) Draw a suitable graph and determine the acceleration from the graph. (b) Check your answer to (a) by making a calculation.
(a) To determine the acceleration from the graph, we need to draw a velocity-time graph.
Let's assume the x-axis represents time (t) in seconds and the y-axis represents velocity (v) in meters per second.
Since the vehicle starts from rest and accelerates uniformly, the graph will be a straight line starting from the origin and sloping upwards.
We know that after 40 seconds, the velocity reaches 60 m/s. So we can plot a point on the graph at (40, 60), representing the final velocity.
The slope of this line will represent the acceleration. Since the vehicle starts from rest, the initial velocity (u) is 0 m/s.
(b) To check our answer, we can calculate the acceleration using the equation:
acceleration (a) = (final velocity (v) - initial velocity (u)) / time (t)
Here, v = 60 m/s, u = 0 m/s, and t = 40 s.
Acceleration (a) = (60 m/s - 0 m/s) / 40 s = 60 m/s / 40 s = 1.5 m/s²
Thus, the acceleration from the graph and the calculated acceleration are both 1.5 m/s².