Speed, Velocity and Acceleration വേഗം · പ്രവേഗം · ത്വരണം
Newton's laws are about how forces change motion. To talk about changes in motion we need exact words: distance and displacement, speed and velocity, acceleration and retardation. You also need to change km/h into m/s, because almost every numerical in this chapter needs it. This page builds all of these from scratch.
- Forces as arrows and the + / − sign for direction (page 1).
- Simple multiplication and division. Fractions like 5/18 are explained below.
1. Distance and displacement
Distance is the total length of the path you actually travel. Displacement (സ്ഥാനാന്തരം) is the straight-line gap between where you started and where you are now, together with its direction. Distance only grows as you move. Displacement can shrink when you turn back, and it is zero when you return to the start.
Ammu walks 400 m east from her home to the shop, then turns back and walks 150 m west to her friend's house. Take east as +. At the end she has walked 550 m (distance), but she is only 250 m east of home (displacement +250 m).
2. Speed and velocity
Speed (വേഗം) tells how fast something moves: the distance covered in one second.
Velocity (പ്രവേഗം) is speed in a stated direction: displacement ÷ time. “15 m/s” is a speed; “15 m/s towards Kochi” is a velocity. Along a straight road we use + and − for the two directions, exactly as with forces. Two autorickshaws going at 10 m/s in opposite directions have the same speed but different velocities, +10 m/s and −10 m/s.
Right (east) is +. The arrow on each vehicle is its velocity. The number without the sign is the speed. In 5 s each vehicle covers speed × 5 metres, in the direction of its arrow.
Speed has only a size. Velocity has a size and a direction. When either the speed or the direction changes, the velocity changes. A uniform velocity (സമപ്രവേഗം) means the same speed and the same direction, i.e. motion along a straight line at a steady speed.
3. Changing km/h into m/s
Speedometers show km/h (kilometres per hour), but physics formulas need m/s. Here is why the conversion factor is 5/18:
- km/h → m/s: multiply by 5/18. 90 km/h = 90 × 5/18 = 25 m/s; 144 km/h = 144 × 5/18 = 40 m/s; 72 km/h = 20 m/s.
- m/s → km/h: multiply by 18/5. 25 m/s = 25 × 18/5 = 90 km/h.
The slider moves in steps of 9 km/h, and each step adds exactly 2.5 m/s. The strip shows how far the vehicle travels in one second. At 90 km/h a bus covers 25 m, about the length of two KSRTC buses, every second!
Forgetting to change km/h into m/s is one of the most common mistakes in this chapter's numericals. Whenever a speed is given in km/h, convert it first.
Worked example 1 · A car on the highway
Q. A car is moving at 90 km/h. Express this velocity in m/s.
Multiply by 5/18. It helps to divide 90 by 18 first.
4. Acceleration
When the velocity of an object changes, it has an acceleration (ത്വരണം): the change in velocity in one second. Call the velocity at the start the initial velocity u (ആദ്യപ്രവേഗം) and the velocity at the end the final velocity v (അന്ത്യപ്രവേഗം). If the change takes time t,
“a = 3 m/s²” means the velocity grows by 3 m/s every second: 0, 3, 6, 9, 12 m/s… The unit m/s² is read “metre per second squared” (metre per second, per second).
The faint pictures are snapshots one second apart. With a positive acceleration the gaps grow (speeding up). With a negative acceleration they shrink (slowing down). A braking vehicle stops when its velocity reaches 0; it does not start going backwards.
Worked example 2 · An autorickshaw starts
Q. An autorickshaw starts from rest and reaches a velocity of 12 m/s in 4 s. Find its acceleration.
“Starts from rest” means u = 0. Use a = (v − u)/t.
5. Retardation: negative acceleration
When an object slows down, the final velocity v is smaller than u, so v − u is negative and the acceleration comes out negative. A negative acceleration (an acceleration opposite to the motion) is called retardation or deceleration (മന്ദീകരണം). We give the retardation as a positive number: an acceleration of −4 m/s² is a retardation of 4 m/s².
A bus at 72 km/h (20 m/s) brakes and stops in 5 s. Its velocity drops 20 → 16 → 12 → 8 → 4 → 0 m/s, losing 4 m/s every second: acceleration −4 m/s², retardation 4 m/s². Standing passengers lurch forward while this happens. Page 7 explains why.
Worked example 3 · The bus brakes
Q. A bus moving at 72 km/h is brought to rest in 5 s by applying the brakes. Find (a) its acceleration and (b) its retardation.
First change 72 km/h into m/s (× 5/18). “Brought to rest” means v = 0. The answer for a will be negative.
6. Uniform velocity and uniform acceleration
Two kinds of motion appear everywhere in this chapter:
- Uniform velocity (സമപ്രവേഗം): the velocity does not change at all. Equal distances in equal times along a straight line, so the acceleration is zero. This is the uniform motion in a straight line (നേർരേഖയിലുള്ള സമചലനം) of Newton's first law.
- Uniform acceleration (സമത്വരണം): the velocity changes by the same amount every second. The gaps between snapshots grow (or shrink) steadily.
Uniform velocity ⇒ acceleration = 0 ⇒ (as you will learn) no unbalanced force. Changing velocity ⇒ acceleration ⇒ an unbalanced force must be acting. This link between acceleration and force is the heart of the chapter.