A particle's position as a function of time t is given by r⃗ =(5.0t+6.0t2)mi^+(7.0−3.0t3)mj^.
2 answers:
The particle's displacement vector has an angle of -65° relative to the positive x-axis.
Additional Details
Acceleration signifies the change in velocity over time.
a = acceleration ( m/s² )
v = final velocity ( m/s )
u = initial velocity ( m/s )
t = time taken ( s )
d = distance ( m )
Now, let's solve the problem!
Data provided:
To find the particle displacement, we need to subtract the two position vectors:
At t = 5.0 seconds,
Further Insights
- Runner's Velocity:
- Kinetic Energy:
- Acceleration:
- Speed of a Car:
Answer Overview
Level: High School
Field: Physics
Topic: Kinematics
Key Terms: Velocity, Driver, Car, Deceleration, Acceleration, Obstacle, Speed, Time, Rate
The particle's position is described as
At t=5 seconds, the position vector reads as
The reference vector when t = 5 seconds is
Let θ denote the angle between the two vectors.
As per definition,
|r₁| = √[175²+(-368)²] = 407.4911
|r₂| = 7
Thus,
θ = cos⁻¹ -2576/(407.4911*7) = cos⁻¹ -0.9031 = 154.57°
Final Result: 154.57°
At t=5 seconds, the position vector reads as
The reference vector when t = 5 seconds is
Let θ denote the angle between the two vectors.
As per definition,
|r₁| = √[175²+(-368)²] = 407.4911
|r₂| = 7
Thus,
θ = cos⁻¹ -2576/(407.4911*7) = cos⁻¹ -0.9031 = 154.57°
Final Result: 154.57°
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Answer:
The answer to your inquiry is Mass = 41230.7 g or 41.23 kg.
Explanation:
Data
Density = 0.737 g/ml
Mass = ?
Volume = 14.9 gal
1 gal = 3.78 l
Process
1.- Convert gallons to liters
1 gal ---------------- 3.78 l
14.9 gal ------------- x
x = 56.44 l
2.- Convert liters to milliliters
1 l ------------------- 1000 ml
56.44 l --------------- x
x = (56.44 x 1000) / 1
x = 56444 ml
3.- Calculate the mass
Formula
Density =
Solving for mass
Mass = density x volume
Substituting values
Mass = 0.737 x 56444
Result
Mass = 41230.7 g or 41.23 kg.
Answer:
Height (h) = 17 m
Velocity (v) = 18.6 m/s
Explanation: This problem can be solved using kinematic motion equations.
Given Data
Initial velocity (u) = 0
Acceleration (a) = g
Time (t) = 1.9 seconds
First, we calculate the height.
Then, we find the final velocity
The acceleration graph is a linear representation described by y=9.8, as it remains constant:
The velocity graph can be represented by y=9.8x (where y signifies velocity and x indicates time):
The displacement graph can be described as y=4.9x^2 (with x as time and y as displacement):
These graphs apply exclusively from x=0 to x=1.9, so disregard other sections of the graphs.
