3.1 - 3.8 Flashcards
whats the gradient of a distance-time graph equal to
the speed
how is average speed found
the total distance travelled / total time taken
how is instantaneous speed found
drawing a tangent on a distance-time graph at the time you want to know its speed at then finding its gradient
define instantaneous speed
the speed at the moment it is measured
define average speed
the rate of change of distance over an entire journey
define scalar
a quantity with only magnitude
define vector
a quantity with magnitude and direction
how can average velocity be found
the displacement/ total time taken
define velocity
the rate of change of displacement
define acceleration
the rate of change of velocity
what can be determined from a velocity-time graph
acceleration: the gradient
displacement: the area under the curve
how can the area of a non-linear graph be determined
by counting the squares that are completely or mostly beneath the curve
what are the SUVAT equations
v= u + at v^2 = U^2 + 2as s= ut +1/2 at^2 s= vt -1/2 at^2 s=1/2(u+v)t
how can the v=u+at equation be derived
from a velocity-time graph where the initial velocity is u and the final velocity is v. the gradient = (v-u)/t. the gradient is the acceleration so this can be rearranged to get v=u+at
how can the s=ut+1/2(at^2) equation be derived
from a velocity-time graph with initial velocity u and final velocity v. split it into a triangle and rectangle. the area of the rectangle is ut and the triangle is 1/2(v-u)t.
from v=u+at you get v-u=at. sub that in to get 1/2at^2. add them together for the total area which equals the displacement(s). s=ut + 1/2(at^2)
how can the s=1/2(u+v)t equation be derived
from a velocity-time graph with initial velocity u and final velocity v. take the area of the trapezium to get 1/2(u+v)t. the area is the displacement(s) so s=1/2(u+v)t
how can the v^2 = u^2 +2as equation be derived
rearrange v=u+at to get t=(v-u)/a. substitute that in to the equation s=1/2(u+v)t and rearrange to get v^2=U^2+2as.
what is stopping distance
the distance travelled in the time it takes the driver to react to a hazard and the car to stop. the sum of the thinking distance and braking distance
define thinking distance
the distance travelled between when a driver first perceives the need to stop and when the brakes are applied
define braking distance
the distance travelled from the time the brakes are applied to the time the vehicle stops
factors affecting stopping distance
vehicle speed, brake conditions, tyre conditions, road conditions, weather conditions, driver alertness
how does projectile motion work
horizontal and verticle components are independent. the horizontal speed remains the same because no force is acting on it. the vertical speed accelerates towards the ground due to gravity.
define projectile motion
the motion of an object thrown into the air subject only to the force of gravity
whats the shape of a displacement-time^2 graph for an object in free fall and why
a straight line through the origin. constant gradient. using s=ut +1/2at^2. u=0 and a=9.81 so it’s s=4.905t^2. 4.905 is constant so s is directly proportional to t^2
