Answer:
a) 1.50 m/s²
b) 675m
c) 11.25 m/s
Step-by-step explanation:
1. a) Acceleration can be found from the gradient of a speed-time graph, which is the graph we have here.
Notice that the graph from t=0 to t=10 has the same gradient thoughout (since it is a straight line). Hence, the acceleration when t=4 is the same as the acceleration from t=0 to t=10.
To find the gradient of the graph from t=0 to t=10, use the gradient formula below:
gradient=[tex] \frac{y1 - y2}{x1 - x2} [/tex]
The coordinates of the point at t=0 is (0,0) and the point at t=10 is (10,15).
Thus, gradient
[tex] = \frac{15 - 0}{10 - 0} \\ = \frac{15}{10} \\ = 1.5[/tex]
Therefore the acceleration when t=4 is 1.50 m/s².
*Acceleration is the rate of change of velocity (or speed).
b) Distance travelled can be found by calculating the area under a speed-time graph.
The area under the graph is the orange trapezium that the question has shaded for you already.
Formula for area of trapezium= ½(a+b)(height)
a+b is the total length of the two parallel horizontal lines of the trapezium.
Let the top line be a and the bottom line be b.
length of a= distance between (10,15) and (40,15)
Length of a
= 40 -10
= 30 units
Length of b
= 60 -0
= 60 units
height of trapezium= 15 units
Area of trapezium
= ½(30 +60)(15)
= 675 units²
Thus, the distance travelled is 675m.
c) Avg speed= total distance ÷ total time
From part b, we know that the total distance travelled is 675m. The total time is 60s since the graph is from t=0 to t=60.
Hence, average speed
= 675 ÷60
= 11.25 m/s
