What is Acceleration? Definition and Formula

Physics · Motion In A Straight Line · NEET

Acceleration is the rate of change of velocity with time. In simple words, it tells you how fast the velocity of an object is changing each second. Its formula is a = (v - u)/t, its SI unit is metre per second squared (m/s^2), and it is a vector. Memory hook: "acceleration = velocity change per second" - if velocity does not change, acceleration is zero even at very high speed.
Acceleration = rate of change of velocity with timevttv - uslope = a = (v - u)/tOn a v-t graph, slope = accelerationa > 0 : speeding upv same dira < 0 : slowing downa opposes vSI unit: m/s^2
On a velocity-time graph, acceleration is the slope of the line: a = (v - u)/t. If a points the same way as velocity the object speeds up; if it opposes velocity the object slows down (retardation). SI unit is m/s^2.

Your doubts, answered

Is acceleration the same as speed or velocity?

No. Speed and velocity tell you HOW FAST an object moves. Acceleration tells you how fast the velocity CHANGES. A car moving at a steady 100 km/h has high speed but zero acceleration, because its velocity is not changing. Acceleration only exists when velocity changes in size or direction.

Can acceleration be zero when the object is moving fast?

Yes. If an object moves with constant velocity (same speed and same direction), its velocity does not change, so a = (v - u)/t = 0. A train cruising at 120 km/h in a straight line has zero acceleration. High speed does not mean high acceleration.

What does negative acceleration mean?

Negative acceleration means the acceleration vector points in the negative direction of your chosen axis. If the object is moving in the positive direction, negative acceleration slows it down (this is called retardation or deceleration). But if the object is already moving in the negative direction, negative acceleration speeds it up. So negative does not always mean slowing down - it depends on the direction of velocity.

Is acceleration a scalar or a vector?

Acceleration is a vector. It has both magnitude (how much) and direction. Because velocity is a vector, its rate of change is also a vector. In one dimension (a straight line), we show direction with a + or - sign instead of arrows, which is why NEET straight-line problems use signs so carefully.

What is the SI unit of acceleration and how do I get it?

The SI unit is metre per second squared, written m/s^2. You get it from the formula: velocity is in m/s, and you divide by time in s, so (m/s) / s = m/s^2. It means the velocity changes by that many m/s every second. For example, 5 m/s^2 means velocity increases by 5 m/s each second.

⚠️ The NEET trap
The object has the largest speed, so it must have the largest acceleration.
Acceleration depends only on how fast velocity CHANGES, not on how large the speed is. An object can have huge speed with zero acceleration (constant velocity), or small speed with huge acceleration (velocity changing quickly).
🧠 NEET loves this: a body moving at constant high velocity has a = 0. Do not confuse a big v with a big a.

Real NEET questions

NEET 2023

A bullet enters a wooden block with speed u and, after travelling 24 cm inside it, its speed reduces to u/3. Assuming uniform retardation, the further distance it travels before coming to rest is:

A · 3 cm
B · 8 cm
C · 12 cm
D · 24 cm
Solution: Use v^2 = u^2 - 2as (uniform acceleration/retardation, so no time needed). Step 1: For the first 24 cm, final speed is u/3, so (u/3)^2 = u^2 - 2a(0.24). This gives u^2/9 = u^2 - 2a(0.24), so 2a(0.24) = u^2 - u^2/9 = (8/9)u^2. Step 2: Find the TOTAL stopping distance L (where final speed = 0): 0 = u^2 - 2aL, so L = u^2/(2a). Step 3: From step 1, 2a = (8/9)u^2 / 0.24, so 2a = (8 u^2)/(9 x 0.24). Then L = u^2 / (2a) = u^2 x (9 x 0.24)/(8 u^2) = (9 x 0.24)/8 = 2.16/8 = 0.27 m = 27 cm. Step 4: Further distance after the first 24 cm = total 27 cm - 24 cm = 3 cm. Answer: A.

Solved Motion In A Straight Line NEET PYQs

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Frequently asked

What is acceleration in one line?

Acceleration is the rate of change of velocity with time, given by a = (v - u)/t, measured in m/s^2.

What is the formula for average acceleration?

Average acceleration = change in velocity / time taken = (v - u)/t, where u is initial velocity and v is final velocity.

What is the SI unit and dimension of acceleration?

The SI unit is m/s^2 and the dimensional formula is [M^0 L^1 T^-2].

Does acceleration mean speeding up?

Not always. Acceleration means velocity is changing. It can mean speeding up, slowing down (retardation), or even just changing direction. Any change in velocity is acceleration.

Can an object have zero velocity but non-zero acceleration?

Yes. At the highest point of a ball thrown up, velocity is zero for an instant, but acceleration equals g (about 9.8 m/s^2 downward) the whole time. This is a common NEET point.