Kinematics

Distance = Speed x Time

Time = Distance / Speed

Speed = Distance / Time

Distance-time graph

Speed = gradient

Remember Formula Using Units E.g.

Units of speed = km/h

Units of gradient = km/h

Speed-time graph

Distance travelled = Area under graph

Acceleration = gradient

Remember Formula using Units: E.g.

Units of distance = m

Units of area under graph = (m/s)s=m

Units of acceleration = m/s^2

Units of gradient = (m/s)/s=m/s^2

Useful Formula:

Area of trapezium = 1/2 x height x (sum of parallel sides)

The formula rhymes! 🙂

Secondary Maths Tuition: Kinematics Question

kinematics-question-o-levels

Solution:

acceleration of car =\frac{12}{6}=2m/s^2

\frac{v}{15-5}=2

v=2\times 10=20

Let T be the time (in seconds) when the car overtakes the truck.

Total distance travelled by car at T seconds = area under graph = \frac{1}{2}(T-5)(2(T-5))

(2(T-5) is the velocity of car at T seconds, it is obtained in the same way as we calculated v.)

Total distance travelled by truck at T seconds = \frac{1}{2}(6)(12)+\frac{1}{2}(15-6)(12+16)+16(T-15)

Equating the two distances will lead to a quadratic equation T^2-26T+103=0

Solving that gives T=21.12s or T=4.876s (rejected as car only starts at t=5)

21.12-5=16.1s (3 s.f.)