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Forces and Motion - Speed, Velocity, and Acceleration

Grade 9IB

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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Speed is a scalar quantity that measures the distance traveled per unit of time, regardless of direction.

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Velocity is a vector quantity that describes the rate of change of displacement, including both magnitude and direction.

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Acceleration is defined as the rate of change of velocity over time. An object accelerates if its speed changes, its direction changes, or both.

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On a distance-time graph, the gradient (slope) of the line represents the speed of the object.

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On a velocity-time graph, the gradient represents the acceleration, while the area under the line represents the total displacement (ss).

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Standard SI units: Speed and Velocity are measured in m/sm/s (or ms−1ms^{-1}), and Acceleration is measured in m/s2m/s^2 (or ms−2ms^{-2}).

📐Formulae

v=dtv = \frac{d}{t}

vavg=ΔsΔtv_{avg} = \frac{\Delta s}{\Delta t}

a=v−uta = \frac{v - u}{t}

Δv=a×t\Delta v = a \times t

💡Examples

Problem 1:

A car accelerates from an initial velocity of 10 m/s10\text{ m/s} to a final velocity of 25 m/s25\text{ m/s} in a time interval of 5 s5\text{ s}. Calculate the acceleration.

Solution:

a=25 m/s−10 m/s5 s=3 m/s2a = \frac{25\text{ m/s} - 10\text{ m/s}}{5\text{ s}} = 3\text{ m/s}^2

Explanation:

Using the acceleration formula a=v−uta = \frac{v - u}{t}, we subtract the initial velocity (uu) from the final velocity (vv) and divide by the time (tt).

Problem 2:

An athlete runs a 400 m400\text{ m} race on a circular track and finishes at the exact same point they started in 50 s50\text{ s}. Calculate their average speed and average velocity.

Solution:

Speed=400 m50 s=8 m/s\text{Speed} = \frac{400\text{ m}}{50\text{ s}} = 8\text{ m/s}, Velocity=0 m50 s=0 m/s\text{Velocity} = \frac{0\text{ m}}{50\text{ s}} = 0\text{ m/s}

Explanation:

Average speed is total distance (400 m400\text{ m}) divided by time. Velocity is displacement divided by time; since the athlete returned to the start, the displacement is 0 m0\text{ m}.

Problem 3:

A train slows down from 30 m/s30\text{ m/s} to a stop with a constant deceleration of 2 m/s22\text{ m/s}^2. How long does it take for the train to stop?

Solution:

t=v−ua=0 m/s−30 m/s−2 m/s2=15 st = \frac{v - u}{a} = \frac{0\text{ m/s} - 30\text{ m/s}}{-2\text{ m/s}^2} = 15\text{ s}

Explanation:

We rearrange the acceleration formula to solve for time: t=v−uat = \frac{v - u}{a}. Note that deceleration is expressed as a negative acceleration (−2 m/s2-2\text{ m/s}^2).