Question

How do you answer the questions in the picture?? Please helppp!!

Answer 1

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=$\frac{y1 - y2}{x1 - x2}$

The coordinates of the point at t=0 is (0,0) and the point at t=10 is (10,15).

Thus, gradient

$= \frac{15 - 0}{10 - 0} \\ = \frac{15}{10} \\ = 1.5$

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