how to solve numerical based on motion chapter and write all the formulaes
Answers
where a,b,c are constants and x is in meters and t is in sec.
1. Find the displacement at t=1 sec
2. Find the velocity at t=0 and t=1 sec
3. Find the acceleration at t=0 and t=1 sec
Solution:
Now first step to attempt such question is to visualize the whole process.Here the object is moving along a straight line and its motion is described by the given equation
Now we
(1) x=? t=1sec
Here by substituting t=1 in given equation we get the answer
x=a(1)+b(1)2+c(1)3
x=a+b+c m
(2) v=? t=0,v=? t=1
Here we are having the displacement equation,so first we need to find out the velocity equation
So here the most suitable formula is
v=(dx/dt)
or v=d(at+bt2+ct3)/dt
or v=a+2bt+3ct2
Substituting t=0 we get
v=a m/s
Substituting t=1 we get
v=a+2b+3c m/s
(3) a=? t=0,a=? t=1
Now we are having the velocity equation,we need to first find the acceleration equation.
So here the most suitable formula is
a=(dv/dt)
or a=d(a+2bt+3ct2)/dt
a=2b+6ct
Substituting t=0 we get
a=2b m/s2
Substituting t=1 we get
a=2b+6c m/s2
Some other good questions for your Assignments
(a) The displacement of the body x(in meters) varies with time t (in sec) as
x=(-2/3)t2 +16t+2
find following
a. what is the velocity at t=0,t=1
b. what is the acceleration at t=0
c. what is the displacement at t=0
d .what will the displacement when it comes to rest
e .How much time it takes to come to rest.
(b) A man runs at a speed at 4 m/s to overtake a standing bus. When he is 6 m behind the door at t=0, the bus moves forward and continues with a constant acceleration of 1.2 m/s2
find the following
a. how long does it take for the man to gain the door
b if in the beginning he is 10m behind the door, will be running at the same speed ever catch up the bus?
Some Videos on how to solve motion in one dimension problem
Important Graph in One-dimensional Motion
A) Position Time Graph
This is a plot of Position and time of an object moving along the straight line. We can find out velocity, speed, distance, and displacement. We can determine acceleration sign from it but cannot determine the value of it
i) Velocity is given by the Slope of the Position time Graph. Velocity is positive if the slope is positive and Velocity is negative if the slope is negative
ii) The numerical value of the Slope without sign gives the speed of the object
iii) Displacement can be calculated using position at the time interval
iv) Displacement-time graph is same as Position Time graph.Distance time can be drawn from position-time graph by the taking the mirror of the image of the position-time graph from the point zero velocity onwards
iv) The slope of the chord drawn to displacement time or distance-time graph gives the average velocity or average speed over the time interval to which the chords corresponds to
v) If the graph is concave up, acceleration is + positive and If the graph is concave down, acceleration is -ve
B) Velocity Time graph
i) The area under the velocity-t
C) Acceleration -time Curve
i) The area under the curve provides the change in velocity
Hope you like this detailed post on how to solve motion in one dimension problem and it helps you in your studies
Explanation: