Question
Explain how acceleration and initial velocity decides trajectory of a motion.
✓
Answer
1. The resultant motion is linear if:
- initial velocity $\overrightarrow{ u }=0$ (starting from rest) and acceleration $\vec{a}$ is in any direction.
- initial velocity $\overrightarrow{ u } \neq 0$ and acceleration $a$ is in line with the initial velocity (same or opposite direction).
2. The resultant motion is circular if initial velocity $\overrightarrow{ u } \neq 0$ and acceleration $\overrightarrow{ a }$ is perpendicular to the velocity throughout.
3. The resultant motion is parabolic if the initial velocity $\overrightarrow{ u }$ is not in line with the acceleration $\overrightarrow{ a }$ and $\overrightarrow{ a }=$ constant. e.g., trajectory of a projectile motion.
4. Similarly, various other combinations of initial velocity and acceleration will result into more complicated motions.
- initial velocity $\overrightarrow{ u }=0$ (starting from rest) and acceleration $\vec{a}$ is in any direction.
- initial velocity $\overrightarrow{ u } \neq 0$ and acceleration $a$ is in line with the initial velocity (same or opposite direction).
2. The resultant motion is circular if initial velocity $\overrightarrow{ u } \neq 0$ and acceleration $\overrightarrow{ a }$ is perpendicular to the velocity throughout.
3. The resultant motion is parabolic if the initial velocity $\overrightarrow{ u }$ is not in line with the acceleration $\overrightarrow{ a }$ and $\overrightarrow{ a }=$ constant. e.g., trajectory of a projectile motion.
4. Similarly, various other combinations of initial velocity and acceleration will result into more complicated motions.
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(b) Speed with which the ball comes up from the ground after third bounce.
(c) Impulse given by the ball to the ground during this bounce.
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[Ans: $0.8, 5.12 m/s, 1.152N s, 4.608 N, 9.216 \times 104 N/m^2$]
→(a) Coefficient of restitution.
(b) Speed with which the ball comes up from the ground after third bounce.
(c) Impulse given by the ball to the ground during this bounce.
(d) Average force exerted by the ground if this impact lasts for $250\ ms$.
(e) Average pressure exerted by the ball on the ground during this impact if contact area of the ball is $0.5\ cm^2$.
[Ans: $0.8, 5.12 m/s, 1.152N s, 4.608 N, 9.216 \times 104 N/m^2$]