Question

What is the ouput of the following graphs?
1. acceleration - time graph
2. acceleration - position graph
3. velocity - position graph
4. velocity - time graph
5.position - time graph.

(Class 11 Physics , Motion in a straight line)
Please mention the outputs for area and slope of the graphs.​

Answer 1

(a) here, velocity is directly proportional to time ,

e.g., v = kt

differentiate with respect to t

dv/dt = acceleration = k

Also, v = kt

dx/dt = kt

∫dx = k∫t.dt

x = kt²/2 [ this shows path is parabolic ]

Hence, velocity - time graph shows the motion of object is accelerating. And trajectory of motion must be parabolic.

(b) velocity is Constant with time,

e.g., v = k ,

differentiate with respect to t

dv/dt = acceleration = 0

Again, v = k

dx/dt = k

∫dx = k∫dt

x = kt [ this shows motion of path is st. Line]

Hence, object moves with uniform motion. Also trajectory of motion is straight line .

(c) here shows, particle rest for some time. Let at t = t₀ particle starts to move with constant acceleration a , where trajectory of motion is parabolic .

here, v = k(t - t₀)

dx/dt = k(t - t₀)

x = k(t²/2 - tt₀) [ parabolic path ]

And dv/dt = a = k [ constant acceleration]

(d) velocity - time graph is parabolic .

Hence, v is directly proportional to square of time.

e.g., v = kt²

dx/dt = kt²

dx = kt².dt

x = kt³/3 + Q

Hence, trajectory of motion increases strictly with increases time.

Also, acceleration , a = dv/dt = 2kt [ vary with time ]

acceleration is variable . It increases with time.

Answer 2

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