A driver of a car travelling at 52 km/h accelerates uniformly in the opposite direction. The car stops in 5 seconds. Another driver going at 3 km/h in another car applies and stops in 10 seconds on the same graph.
i) Plot the graph of speed vs time (car 1).
ii) Solve for the distance travelled by car (car 1).
Answer (1)
Let's solve the problem step-by-step. The problem involves two main components for the first car:
(i) Plotting the speed vs. time graph for Car 1, and (ii) Calculating the distance travelled by Car 1.
(i) Plot the graph of speed vs. time (Car 1)
Step 1: Understand the motion parameters of Car 1.
Initial speed of Car 1, v i = 52 km/h
The car stops in t = 5 seconds .
Final speed, v f = 0 km/h .
Step 2: Convert units for consistency.
Convert speed from km/h to m/s:
v i = 52 km/h × 1 km 1000 m × 3600 s 1 h = 3600 52 × 1000 ≈ 14.44 m/s
Step 3: Calculate the acceleration using the formula:
a = t v f − v i = 5 0 − 14.44 = − 2.888 m/s 2
Step 4: Plot the graph.
At t = 0 , v = 14.44 m/s
At t = 5 , v = 0 m/s
The graph is a straight line with a negative slope of − 2.888 m/s 2 .
(ii) Solve the distance traveled by Car 1
To find the distance traveled, use the formula for the distance during constant acceleration:
d = v i ⋅ t + 2 1 a ⋅ t 2
Plug in the values:
d = 14.44 × 5 + 2 1 × ( − 2.888 ) × 5 2
d = 72.2 + 2 1 × ( − 2.888 ) × 25
d = 72.2 − 36.1
d = 36.1 meters
Thus, Car 1 travels a distance of 36.1 meters before coming to a stop.
