Question

7. The following table describes the distance covered by a body moving along a straight line to north direction for the first 10 seconds.

S(m) 0 20 40 60 80 100
t(s) 0 2 4 6 8 10



Based on the information given in the table,
(a) Plot the distance against time graph using square sheet.
(b) Compute the velocity of the car.
(c) Plot the velocity against time graph of the car using square sheet.
(d) Determine the initial position of the car

Answer 1

Given the table
t (s): 0, 2, 4, 6, 8, 10
S (m): 0,20,40,60,80,100

Observations: S increases linearly with t. The motion is uniform (constant speed) to the north.

(a) How to plot S vs t on squared paper
- Choose scales that fit the data nicely. A convenient choice:
- x-axis (time): 1 cm = 1 s → x from 0 to 10 cm.
- y-axis (distance): 1 cm = 10 m → y from 0 to 10 cm (0 to 100 m).
- Label axes: horizontal axis "t (s)", vertical axis "S (m)".
- Plot the points: (0,0), (2,20), (4,40), (6,60), (8,80), (10,100). With the chosen scale these are at:
- (0 cm, 0 cm), (2 cm, 2 cm), (4 cm, 4 cm), (6 cm, 6 cm), (8 cm, 8 cm), (10 cm, 10 cm).
- Join the points with a straight line — you will get a straight line through the origin.

(b) Compute the velocity
- Velocity = slope = ΔS / Δt.
- Using any two points, e.g. (0,0) and (10,100): v = (100 − 0) m / (10 − 0) s = 10 m/s.
- So the car’s speed is 10 m/s to the north (constant).

(c) How to plot v vs t on squared paper
- Use the same time scale as for S vs t (1 cm = 1 s).
- For velocity axis use e.g. 1 cm = 1 m/s so the vertical axis goes to 10 cm for 10 m/s.
- Plot a horizontal line at v = 10 m/s from t = 0 to t = 10 s (points (0,10), (10,10)). Label vertical axis "v (m/s)". This is a constant (flat) line.

(d) Initial position
- From the table S(0) = 0 m. So the initial position (relative to the chosen origin) is 0 m (at the origin), i.e. at the reference point, 0 m north.