**(B) Speed – Time Graph**

**1.**The gradient of a speed-time graph is the rate of change of speed or

acceleration.

**2.**

**(a)**From

*O*to

*P*: Gradient = positive → (Speed of object increasing or accelerating).

**(b)**From

*P*to

*Q*: Gradient = 0 → (Object is moving at uniform speed).

**(c)**From

*Q*to

*R*: Gradient = negative → (Speed of object decreasing or decelerating).

**Example:**

**(a)**the rate of speed change when the car travel from

*X*to

*Y*.

**(b)**the rate of speed change when the car travel from

*Y*to

*Z*.

*Solution:***(a)**

Rate of speed change when the car travels from

*X*to*Y*= Gradient

$\begin{array}{l}=\frac{{y}_{2}-{y}_{1}}{{x}_{2}-{x}_{1}}\\ =\frac{5-20}{4-0}\\ =-\frac{15}{4}{\text{ms}}^{-2}\leftarrow \overline{)\begin{array}{l}\text{Negative gradient indicates}\\ \text{that the speed is decreasing}\text{.}\end{array}}\end{array}$

**(b)**

Rate of speed change when the car travels from

*Y*to*Z*= Gradient

$\begin{array}{l}=\frac{{y}_{2}-{y}_{1}}{{x}_{2}-{x}_{1}}\\ =\frac{10-5}{5-4}\\ =5{\text{ms}}^{-2}\end{array}$