What is the nature of velocity-time graph for a car moving with uniform acceleration?
- (a)Parabola
- (b)Logarithmic
- (c)Straight line
- (d)Exponential
Correct — C, Straight line. Uniform acceleration means the velocity changes by the same amount in every equal interval of time, which is written v = u + at. Compare that with the equation of a line, y = mx + c — velocity plays the part of y, time the part of x, the acceleration a is the constant slope and the initial velocity u is the intercept. A relation of that form always plots as a straight line, sloping upward for positive acceleration and downward for retardation.
- (a)Parabola — A parabola is the shape of the displacement-time graph under uniform acceleration, because s = ut + half a t squared has a t squared term. The velocity-time graph has no squared term.
- (b)Logarithmic — A logarithmic curve would mean the velocity rises ever more slowly with time, so the acceleration would be falling — the opposite of uniform acceleration.
- (d)Exponential — An exponential curve would mean the rate of change of velocity itself keeps growing, so the acceleration would not be constant.
Motion graphs encode the calculus of motion in a picture. On a velocity-time graph the slope at any instant is the acceleration and the area under the curve between two instants is the displacement over that interval. Constant acceleration therefore means constant slope, which is precisely a straight line.
The parabola option is the intended trap, because a uniformly accelerating car really does trace a parabola — but on the displacement-time graph, not the velocity-time graph. Read the axis labels first. A quick test that never fails is to ask what is constant. If acceleration is constant the velocity-time plot is straight; if velocity is constant the displacement-time plot is straight and the velocity-time plot is a horizontal line.
- For uniform acceleration, v = u + at, which is linear in time.
- The slope of a velocity-time graph gives the acceleration; the area under it gives the displacement.
- The displacement-time graph for uniform acceleration is a parabola, since s = ut + half a t squared.
- For uniform velocity the acceleration is zero, so the velocity-time graph is a horizontal straight line.
Velocity is linear in time under uniform acceleration, so the graph is a straight line — option (c).
- Answering 'parabola' by recalling the displacement-time graph instead of the velocity-time graph.
- Forgetting that retardation still gives a straight line, only with a negative slope.
A one-line kinematics item; identify which equation governs the named pair of axes, then read off its shape.
If an object moves at a non-zero constant acceleration for a certain interval of time, then the distance it covers in that time
- (a) depends on its initial velocity.
- (b) is independent of its initial velocity.
- (c) increases linearly with time.
- (d) depends on its initial displacement.
Answer(a) depends on its initial velocity.
The same uniform-acceleration equations, asked about distance instead of the graph — and its wrong option (c) is exactly the linear-versus-parabolic confusion tested here.
At uniform speed the acceleration is
- (a) Maximum
- (b) Minimum
- (c) Zero
- (d) Constant
Answer(c) Zero
The limiting case of the same graph — zero acceleration flattens the velocity-time straight line into a horizontal one.
- practice — not a real PYQ
The area under a velocity-time graph gives the
- (a)acceleration
- (b)displacement
- (c)average speed
- (d)jerk
Answer(b) displacement — the slope of the same graph gives the acceleration.
- practice — not a real PYQ
For a body moving with uniform velocity, the velocity-time graph is
- (a)a straight line through the origin
- (b)a straight line parallel to the time axis
- (c)a parabola
- (d)an exponential curve
Answer(b) a straight line parallel to the time axis — zero slope means zero acceleration.