Question

questions 5-10 refer to displacement - time graph of a carts motion:

1. in which section(s) is the cart accelerating?
2. in which section(s) is the cart not moving?
3. in which section(s) is the cart moving backwards?
4. in which section(s) is the carts instantaneous velocity at any time equal to its average velocity?
5. what is the velocity of the cart in these sections? a - b ____ c - d __ e - f __ f - g ____
6. how far does the cart move in section b - c? ____ e - f? ____ physicsfundamentals

Explanation:

Step1: Recall velocity - displacement graph relationship

Velocity is slope of displacement - time graph. Acceleration is change in velocity.

Step2: Analyze acceleration

The cart is accelerating where the slope of the displacement - time graph is changing. In sections 'c - d' and 'd - e', the slope is changing. So for question 5, the answer is 'c - d, d - e'.

Step3: Analyze non - moving state

The cart is not moving when the displacement is constant (slope = 0). In section 'a - b' and 'e - f', the slope is 0. So for question 6, the answer is 'a - b, e - f'.

Step4: Analyze backward motion

The cart is moving backwards when the displacement is decreasing with time (negative slope). In section 'f - g', the slope is negative. So for question 7, the answer is 'f - g'.

Step5: Analyze equal instantaneous and average velocity

The instantaneous velocity is equal to the average velocity when the motion is uniform (constant slope). There are no such sections in this graph. So for question 8, the answer is 'None'.

Step6: Calculate velocities

For 'a - b': slope = 0, so velocity = 0. For 'c - d': slope=$\frac{40 - 30}{40 - 25}=\frac{10}{15}=\frac{2}{3}\text{ m/s}$. For 'e - f': slope = 0, so velocity = 0. For 'f - g': slope=$\frac{20 - 60}{70 - 60}=- 4\text{ m/s}$.

Step7: Calculate displacements

For 'b - c': displacement = 40 - 10 = 30 m. For 'e - f': displacement = 60 - 60 = 0 m.

Answer:

1. c - d, d - e
2. a - b, e - f
3. f - g
4. None
5. a - b: 0 m/s; c - d: $\frac{2}{3}$ m/s; e - f: 0 m/s; f - g: - 4 m/s
6. b - c: 30 m; e - f: 0 m