Grade 10 · Core Mathematics · Lesson 14 of 14

Real-Life Applications of Linear Motion

A Grade 10 Core Mathematics CBE lesson from the sub-strand Linear Motion. In it, learners construct and interpret velocity-time graphs for vertical rocket acceleration, missile flight, and car braking efficiency tests.

Strand Measurements and GeometrySub-strand Linear MotionLesson code 10CM-29-L1440 minutes · 3 slides

KICD learning outcome (h)

Appreciate use of linear motion in real-life situations.

By the end of this lesson, learners should be able to

Construct and interpret velocity-time graphs for vertical rocket acceleration, missile flight, and car braking efficiency tests.
Calculate relative speeds and exact meeting clock times for vehicles and runners moving towards each other.
Solve overtaking problems involving delayed departures and extended bodies on parallel tracks.

Key vocabulary

Deceleration: The rate at which an object slows down over a period of time.; A rally car experiences a deceleration of $10 {m/s}^{2}$ when full brakes are applied.
Relative speed: The speed of one object measured with respect to another moving object.; Two approaching vehicles at $70 km/h$ and $80 km/h$ have a relative speed of $150 km/h$ .
Head start: The initial distance lead gained by an object departing before another.; A cyclist leaving one hour earlier gains a $15 km$ head start over a matatu.

Lesson preview

Slide 1 · Velocity-Time Graphs in Extreme SituationsModel · 12 min

Figure 1: A velocity-time graph for a braking rally car, showing an initial velocity of 50 m/s decreasing to zero over 5 seconds.

Velocity-time graphs allow us to analyse complex physical phenomena such as vertical rocket launches, missile or drone test flights, and vehicle braking tests. For vertical acceleration, velocity increases as a rocket ascends skyward. Conversely, applying brakes causes a decrease in velocity down to zero. The area bounded by the graph line and the time axis gives the total distance or altitude gained. Use Figure 1 to see how the area under a braking velocity-time graph gives the total distance.

Vertical rocket launches exhibit uniform vertical acceleration represented by an upward-sloping velocity-time line.
Braking efficiency tests produce a downward-sloping line as vehicle velocity decreases to zero over time.
The vertical axis measures velocity in metres per second while the horizontal axis records time.
The geometric area beneath a velocity-time line measures total displacement or height reached during motion.

Worked example. Identify initial velocity

u = 50 m/s

, final velocity

v = 0 m/s

, and time

t = 5 s

. Calculate deceleration:

a = \frac{v - u}{t} = \frac{0 - 50}{5} = - 10 {m/s}^{2}

. (Deceleration is

10 {m/s}^{2}

). Calculate distance using the area under the triangular velocity-time graph:

Area = \frac{1}{2} \times base \times height = \frac{1}{2} \times 5 \times 50 = 125 metres

. Answer: Deceleration is $10 {m/s}^{2}$ ; distance covered during braking is $125 metres$ . Since $125 m$ is less than $130 m$ , the car safely stopped within the limit..

Check question: A weather rocket is launched vertically, reaching a velocity of $300 m/s$ after $15 seconds$ of uniform acceleration. What height does it reach during these $15 seconds$ ?

$20 m$
$150 m$
$2250 m$
$4500 m$

Show answer

$2250 m$ . The height reached during uniform vertical acceleration is the area of the triangle under the velocity-time graph: $\frac{1}{2} \times base \times height = \frac{1}{2} \times 15 \times 300 = 2250 m$ .

Slide 2 · Relative Speed for Approaching ObjectsPractice · 14 min

Figure 2: A matatu and a car travelling towards each other between Nakuru and Nairobi, showing their combined relative speed.

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Homework and the other 13 lessons in this sub-strand

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Real-Life Applications of Linear Motion

By the end of this lesson, learners should be able to

Key vocabulary

Lesson preview

Teach the full lesson on the projector

All 14 lessons in Linear Motion