TUTORBEE
Word Problems
MCV 4U – Calculus and Vectors
Applications of Derivatives
Winter 2016
Linear Motion of a Particle
13.
The position function 𝑠 𝑡 of a particle moving along an 𝑥 axis is 𝑠 𝑡 = 4.0 − 6.0𝑡 * , with 𝑠 in
metres and 𝑡 in seconds.
a)
At what time and where does the particle momentarily stop?
b)
At what time does the particle pass through the origin?
14.
If a particle’s position is given by 𝑠(𝑡) = 4 − 12𝑡 + 3𝑡 * (where 𝑡 is in seconds and 𝑥 is in metres),
what is its velocity at 𝑡 = 1𝑠? Is it moving in the positive or negative direction?
b)
Is the speed increasing or decreasing?
c)
Is there a time when the velocity is zero?
15.
The position of a particle moving along the 𝑥 axis is given in centimetres by 𝑠 𝑡 = 9.75 + 1.50𝑡 6 ,
where 𝑡 is in seconds. Calculate:
a)
the average velocity during the time interval 𝑡 = 2.00𝑠 to 𝑡 = 3.00𝑠.
b)
the instantaneous velocity at 𝑡 = 2.00𝑠.
c)
the instantaneous velocity when the particle is midway between its positions at 𝑡 = 2.00𝑠 and 𝑡 =
3.00𝑠
16.
If the position of a particle is given by 𝑠 𝑡 = 20𝑡 − 5𝑡 6 , where 𝑥 is in metres and 𝑡 is in seconds,
when, if ever, is the particle’s velocity zero?
b)
When is its acceleration zero?
c)
For what time range is the acceleration negative?
17.
The position of a particle moving along an 𝑥 axis is given by 𝑠 𝑡 = 12𝑡 * − 2𝑡 6 , where 𝑥 is in
metres and 𝑡 is in seconds. Determine the position, velocity and acceleration of the particle at 𝑡 =
3.0𝑠.
b)
When is the object speeding up and slowing down?
c)
When is the maximum possible speed velocity reached?
d)
Determine the average velocity between 𝑡 = 0.00𝑠 and 𝑡 = 3.00𝑠
18.
The position function 𝑠 𝑡 of a particle moving along an 𝑥 axis is 𝑠 𝑡 = 0.5𝑡 7 − 4𝑡 6 + 5𝑡 * + 13,
with 𝑠 in metres and 𝑡 in seconds.
a)
Find the initial position, velocity and acceleration of the particle.
b)
Find the distance travelled by the object after 8 seconds.