The graph given alongside shows how the speed of a car changes with time:
(1) What is the initial speed of the car?
(2) What is the maximum speed attained by the car?
(3) Which part of the graph shows zero acceleration?
(4) Which part of the graph shows varying retardation?
(5) Find the distance travelled in the first 8 hours.
The graph given alongside shows how the speed of a car changes with time:
(1) What is the initial speed of the car?
(2) What is the maximum speed attained by the car?
(3) Which part of the graph shows zero acceleration?
(4) Which part of the graph shows varying retardation?
(5) Find the distance travelled in the first 8 hours.
Step 1: Given that:
Step 2: 1) Calculation of initial speed of the car:
By the graph,
At time, t=0 ; the speed of the car= 10kmh−1
Thus, the initial speed of the car is 10kmh−1.
Step 3: 2) Calculation of the maximum speed attained by the car:
From the graph, it is seen that;
At points B and C the car has a maximum speed.
The speed of the car at B and C= 35kmh−1
Thus, the maximum speed attained by the car = 35kmh−1
Step 4: 3) Determination of the part of the graph of zero acceleration:
When the speed of the body, does not change with time, it is said that the body has zero acceleration.
From the graph, it is clear that between points B to C the speed of the car is constant.
Therefore between points B to C, the car has zero acceleration.
Step 5: 4) Determination of the part of the graph of varying retardation:
When the final speed of a body is less than the initial speed then the rate of change in speed is negative, and it is termed as retardation or negative acceleration.
If the rate of change in speed varies with time then the body possesses a varying acceleration or retardation.
From the graph it is seen that;
From points, C to D the car has a varying retardation.
Step 6: 5) Calculation of the distance travelled in the first 8 hours:
The area of speed time graph= The distance covered by the body
From the graph, in the first 8 hours, the distance covered by the car can be calculated by finding the area of the graph in 8 hours.
The distance travelled in the first 8 hours = The area of trapezium OABE+ Area of the rectangle BCFE
= 12×(OA+BE)×OE+BE×BC
= 12×(10kmh−1+35kmh−1)×3hrs+35kmh−1×(8hrs−3hrs)
= 45×32+35×5
= 1352+175
= 67.5+175
= 242.5km
Thus, the distance travelled by car in the first 8hrs is 242.5km .
Thus,
1) The initial speed of the car = 10kmh−1
2) The maximum speed attained by the car= 35kmh−1
(3) The part of the graph that shows zero acceleration= From B to C
(4) The part of the graph that shows varying retardation= From C to D
(5) The distance travelled in the first 8 hours = 242.5km
Step 1: Given that:
Step 2: 1) Calculation of initial speed of the car:
By the graph,
At time, t=0 ; the speed of the car= 10kmh−1
Thus, the initial speed of the car is 10kmh−1.
Step 3: 2) Calculation of the maximum speed attained by the car:
From the graph, it is seen that;
At points B and C the car has a maximum speed.
The speed of the car at B and C= 35kmh−1
Thus, the maximum speed attained by the car = 35kmh−1
Step 4: 3) Determination of the part of the graph of zero acceleration:
When the speed of the body, does not change with time, it is said that the body has zero acceleration.
From the graph, it is clear that between points B to C the speed of the car is constant.
Therefore between points B to C, the car has zero acceleration.
Step 5: 4) Determination of the part of the graph of varying retardation:
When the final speed of a body is less than the initial speed then the rate of change in speed is negative, and it is termed as retardation or negative acceleration.
If the rate of change in speed varies with time then the body possesses a varying acceleration or retardation.
From the graph it is seen that;
From points, C to D the car has a varying retardation.
Step 6: 5) Calculation of the distance travelled in the first 8 hours:
The area of speed time graph= The distance covered by the body
From the graph, in the first 8 hours, the distance covered by the car can be calculated by finding the area of the graph in 8 hours.
The distance travelled in the first 8 hours = The area of trapezium OABE+ Area of the rectangle BCFE
= 12×(OA+BE)×OE+BE×BC
= 12×(10kmh−1+35kmh−1)×3hrs+35kmh−1×(8hrs−3hrs)
= 45×32+35×5
= 1352+175
= 67.5+175
= 242.5km
Thus, the distance travelled by car in the first 8hrs is 242.5km .
Thus,
1) The initial speed of the car = 10kmh−1
2) The maximum speed attained by the car= 35kmh−1
(3) The part of the graph that shows zero acceleration= From B to C
(4) The part of the graph that shows varying retardation= From C to D
(5) The distance travelled in the first 8 hours = 242.5km
