Math topic中文

Kinematics

application of differentiation and integration to problems involving displacement, velocity and acceleration of a particle moving in a straight line

Practice questions

1A bird is sitting on the top, $T$ , of a vertical pole 20 m above the ground and the angle of elevation of the bird at $T$ …
2A particle starts from rest from a point $O$ and moves in a straight line such that its velocity $v$ m/s, is given by $v = 24t - 6t^2$ …
3A motorist, travelling at a constant velocity of V m/s, passed a fixed point X and saw few vehicles ahead. He stepped on…
4A particle, P, starts moving in a straight line with a velocity of 8 m/s at a displacement of 3 m from a fixed point O.…
5A particle $P$ moves in a straight line so that, $t$ seconds after passing through a fixed point $O$ , its velocity $v$ m…
6A particle moves in a straight line, so that, $t$ seconds after leaving a fixed point $O$ its velocity, $v$ is given by…
7A particle passes a fixed point $O$ and moves in a straight line such that, $t$ s after leaving $O$ , its velocity, $v\text{ m/s}$ …
8A particle moves in a straight line such that its velocity, $v\text{ m/s}$ , is given by $v = 9\sin\left(\frac{t}{2}\right)$ …
9 $P$ , $Q$ , $R$ and $S$ are four villages located on an island, where $Q$ is due north of $R$ . $PQ = 924\text{ m}$ , $QR = 640\text{ m}$ …
10A particle P moves along a horizontal straight line so that t seconds after motion has begun, its displacement, s m, fro…
11A particle moves in a straight line so that its velocity, $v$ m/s is given by $v = t^2 - 4t + 3$ , where $t$ is the time…
12A particle travels in a straight line so that, $t$ seconds after leaving a fixed point $O$ , its velocity, $v\text{ m s}^{-1}$ …
13A particle moves in a straight line and its initial velocity is 21 cm/s. After $t$ seconds, its acceleration, $a$ cm/s $^2$ …
14A cyclist moves along a straight road from home $O$ . His velocity, $v\text{ m/min}$ , is given by $v = 25 + 10t - 3t^2$ ,…
15In the binomial expansion of $\left(x + \frac{k}{x}\right)^5$ , where $k$ is a positive integer, the coefficients of $\frac{1}{x^3}$ …
16A particle P starts from rest at a fixed point O and moves in a straight line. The velocity, $v\ \text{ms}^{-1}$ , of the…
17Nurul took 2.5 hours to travel at a constant speed from Town $A$ to $B$ . On her journey back, she increased her constant…
18A particle moves in a straight line such that, $t$ s after passing through a fixed point $O$ , its displacement from $O$ …
19A particle $P$ travels in a straight line and its velocity, $v$ m/s, is given by $v = 4\sin^2\left(\frac{t}{2}\right) - 1$ …
20A particle moving in a straight line, passes through a fixed point $O$ with a velocity of $4\text{ m/s}$ . Its accelerati…
21A particle $P$ moves in a straight line, so that, $t$ seconds after leaving a fixed point $O$ , its velocity, $v$ m/s, is…
22A particle moves from point P towards point O. The speed of the particle, $t$ seconds after passing point P, can be mode…
23A ferris wheel with a radius of 15 m completes one rotation every 3 minutes. Passengers get onto the ferris wheel at the…
24A scooter travelling up and down a straight horizontal road passes a fixed point O with a speed of $p\ \text{m s}^{-1}$ .…
25The diagram shows the speed-time graph for a car journey. Find the speed of the car when $t = 8$ . Answer ... m/s Find th…
26A particle moves in a straight line with a fixed point $O$ . The velocity of the particle, $v$ m/s, is given by $v = \dfrac{25}{2t+1} + 10$ …
27A particle $X$ travels in a straight line so that $t$ seconds after leaving a fixed point $O$ , its velocity $v$ m/s, is…
28A particle moves in a straight line, so that $t$ seconds after passing through a fixed point $O$ , its acceleration, $a\text{ ms}^{-2}$ …
29A particle starts from a point O and moves in a straight line so that its velocity, $v$ m/s, is given by $v = 5 - e^{3-2t}$ …
30A particle travels in a straight line, so that $t$ seconds after passing a fixed point $O$ , its velocity, $v$ m/s, is gi…
31A particle starts from rest at a fixed point $O$ and moves in a straight line towards a point $A$ . Its velocity, $v$ m/s…
32A particle moves in a straight line so that, $t$ seconds after leaving a fixed point $O$ , its velocity $v\text{ ms}^{-1}$ …
33A particle moves from rest at $A$ and comes to rest at $B$ . Its speed, in m/s, when travelling from $A$ to $B$ is given…
34A cyclist starts from rest from a point $A$ and travels in a straight line until she comes to a rest at a point $B$ . Dur…
35A particle moves in a straight line so that t seconds after leaving a fixed point O, its velocity v m/s, is given by $v = 16\bigl(2e^{-2t} - e^{-t}\bigr)$ …
36A particle travelling in a straight line passes through a fixed point $O$ with a velocity of 3 m/s. The acceleration, $a$ …
37A particle P moves in a straight line and passes through a fixed point O so that its velocity, v m/s is given by $v = t^2 - 5t + 4$ …
38A dot on a computer screen moves in a straight line and passes through a fixed point $A$ . The distance, $d$ metres, that…
39A particle, P, travels in a straight line so that at time t seconds, its velocity, v m/s, is given by $v = \cos\left(\dfrac{\pi}{4}t + \dfrac{\pi}{6}\right)$ …
40The diagram shows a circle, with centre $O$ , passing through $A$ , $B$ , $C$ , $D$ and $E$ . $CG$ and $FG$ are tangents to t…
41The velocity, $v\text{ ms}^{-1}$ , of a particle moving in a straight line, $t$ seconds after passing a fixed point $O$ ,…