With s(t) as displacement, velocity is ds ÷ dt and acceleration is dv ÷ dt, so this IB sheet opens by differentiating position twice. The key records 12 m/s as a velocity value and v = 0 for the instant a particle stops.
Key Takeaways
Velocity is ds ÷ dt when s(t) is displacement (Q1).
Acceleration is dv ÷ dt (Q2).
Q5 records v = 0 at the moment a particle stops.
Section A: Multiple Choice Questions (1 Mark Each)
Choose the correct option for each question.
1.If s(t) is the displacement, then the velocity is given by
(a) ds ÷ dt(b) d²s ÷ dt²(c) ∫s dt(d) dθ ÷ dt
2.The acceleration is given by
(a) dv ÷ dt(b) ∫v dt(c) ds ÷ dt(d) v × t
3.If v = 3t², then at t = 2 s the velocity is
(a) 12 m/s(b) 6 m/s(c) 18 m/s(d) 9 m/s
4.The displacement is obtained from the velocity by
(a) integration(b) differentiation(c) multiplying by time(d) finding the gradient
5.A particle is instantaneously at rest when
(a) v = 0(b) a = 0(c) s = 0(d) t = 0
6.If the displacement is s = t² + 3t, then the velocity is
(a) 2t + 3(b) 2t(c) t² + 3(d) 2t² + 3t
Section B: Short Answer Type Questions (2 Marks Each)
Show all steps clearly.
7.How do you find the velocity from the displacement?
8.How do you find the acceleration from the velocity?
9.How do you find the displacement from the velocity?
10.If v = 0 at a certain time, what does this mean for the motion?
11.Write the expression for the velocity if s = 2t² − 5t.
12.What does a = 0 mean for the motion?
13.How do you find the distance travelled when the velocity is constant?
14.If s = t³, find the velocity as a function of t.
Section C: Numericals & Word Problems (3 Marks Each)
Apply the concepts to solve the problems. Show all working.
15.If s = 3t² + 2t, find the velocity using v = ds ÷ dt.
16.If v = 4t + 3 and s = 0 when t = 0, find s by integrating.
17.If s = t² − 4t, find the time when the particle is at rest (v = 0).
18.If v = 6t, find the acceleration using a = dv ÷ dt.
19.If s = t³ − 3t, find the velocity at t = 2.
20.A particle moves with constant acceleration a = 4. If v = 0 when t = 0, find v by integrating.
Answer Key
1. a) ds ÷ dt
2. a) dv ÷ dt
3. a) 12 m/s
4. a) integration
5. a) v = 0
6. a) 2t + 3
7. Refer to solution guide.
8. Refer to solution guide.
9. Refer to solution guide.
10. Refer to solution guide.
11. Refer to solution guide.
12. Refer to solution guide.
13. Refer to solution guide.
14. Refer to solution guide.
15. Refer to solution guide.
16. Refer to solution guide.
17. Refer to solution guide.
18. Refer to solution guide.
19. Refer to solution guide.
20. Refer to solution guide.
End of Worksheet
People Also Ask
How is velocity found from displacement?
As ds ÷ dt, option (a) in this worksheet (Q1).
How is acceleration found?
As dv ÷ dt, option (a) in this worksheet (Q2).
What is the velocity when a particle comes to rest?
v = 0, option (a) in this worksheet (Q5).
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