Uniform Motion in a Straight Line

1. Introduction

Uniform motion in a straight line occurs when a body moves along a straight path with constant speed and unchanging direction.
In this case, the velocity remains constant.

[v = \dfrac{\Delta s}{\Delta t} = \text{constant}]

Where [v] is velocity, [\Delta s] is displacement, and [\Delta t] is time interval.

2. SI Unit and Dimensional Formula

SI Unit: [m/s]
Dimensional Formula: [M^0 L^1 T^{-1}]

3. Key Points

Displacement is proportional to time: [s \propto t]
The position–time graph is a straight line.
Acceleration is zero.
Distance covered = magnitude of displacement (since motion is straight and direction does not change).

4. Important Formulas to Remember

No.	Formula	Description
1	[v = \dfrac{\Delta s}{\Delta t}]	Constant velocity for uniform motion.
2	[s = s_0 + vt]	Position at time t, where [s_0] = initial position.
3	[t = \dfrac{\Delta s}{v}]	Time taken to cover displacement [\Delta s].

5. Practice Questions

Solved Examples

1. A car moves with a uniform velocity of 20 m/s. How much distance will it cover in 15 s?

Solution: [s = vt = 20 \times 15 = 300 \, \text{m}]

2. A train covers 120 km in 2 hours with uniform motion. Find its velocity.

Solution: [v = \dfrac{120}{2} = 60 \, \text{km/h}]

3. A body starts from position s = 5 m and moves with uniform velocity 4 m/s. Find its position after 10 s.

Solution: [s = s_0 + vt = 5 + (4 \times 10) = 45 \, \text{m}]

4. A cyclist moves at uniform velocity and covers 18 km in 0.5 hours. Find the speed in m/s.

Solution: Convert 0.5 h = 1800 s, 18 km = 18000 m ⇒ [v = \dfrac{18000}{1800} = 10 \, \text{m/s}]

5. A car moves with uniform velocity 25 m/s. How long will it take to cover 1 km?

Solution: [t = \dfrac{\Delta s}{v} = \dfrac{1000}{25} = 40 \, \text{s}]

Conceptual Questions

1. What is uniform motion in a straight line?

Motion in which a body moves along a straight path with constant velocity.

2. Is acceleration present in uniform motion?

No. Acceleration is zero because velocity is constant.

3. What does the slope of the position–time graph represent in uniform motion?

The slope represents constant velocity.

4. Can a body have uniform motion if its speed changes but direction remains straight?

No. Uniform motion requires constant speed along a straight line.

5. How are distance and displacement related in uniform straight-line motion?

They are equal because motion is along a straight path in one direction.

7. FAQs / Common Misconceptions

1. Does uniform motion mean the body is stationary?

No. Uniform motion means constant velocity, not zero velocity.

2. Can a body move in a curved path and still have uniform motion?

No. Uniform motion must be along a straight line.

3. Is speed the same as velocity in uniform motion?

Magnitude of velocity = speed, but velocity is a vector; in straight-line motion, they have the same magnitude.

4. Can a body have uniform motion if it accelerates?

No. Acceleration must be zero for uniform motion.