Kinematics on a line Problem set B Answers

1. (a) \(v = 15\cos 3t\), \(a = −45\sin 3t\)
2. (b) \(v = −8e^{-4t}\), \(a = 32e^{-4t}\)
3. (c) \(v = 15 (5t - 2)^{2}\), \(a = 750t - 300\)

1. (a) \(a = 4s + 10\)
2. (b) \(a = 2s^{3} - 12s\)
3. (c) \(a = 2e^{4s}\)

1. (a) 14.5 m s⁻¹
2. (b) 1.20 m

1. (a) −0.873 m s⁻¹
2. (b) 3.20 m s⁻²

1. (a) \(a = 4s - 36\)
2. (b) −16 m s⁻². Negative: the boat is slowing down.

1. (a) 7.34 m s⁻¹
2. (b) 15.3 m s⁻¹

1. (a) \(a = −48\cos 4t\)
2. (b) \(k = −16\)

\(a = −4s\)