# An object with a mass of #2 kg# is acted on by two forces. The first is #F_1= <4 N , 8 N># and the second is #F_2 = < 1 N, 7 N>#. What is the object's rate and direction of acceleration?

##### 1 Answer

The objects rate of acceleration is

The direction of the acceleration is at an angle of

#### Explanation:

Let the resultant force acting on the object be

# vecF = vecF_1 + vecF_2#

# \ \ \ \ = <<4,8>> + <<1,7>>#

# \ \ \ \ = <<5,15>>#

The magnitude,

# F = | vecF | #

# \ \ \ \= |<<5,15>>| #

# \ \ \ \= sqrt(5^2+15^2) #

# \ \ \ \= sqrt(25+225) #

# \ \ \ \= sqrt(250) #

# \ \ \ \= 15.81 \ N # (2dp)

Applying Newton's 2nd Law of Motion,

# :. 15.81=2a#

# :. a=7.91 \ ms^-2# (2dp)

The direction of the acceleration is the same as the direction of the resultant force

# tan theta = 15/5 #

# :. \ theta = arctan 3#

# :. \ theta = 71.6º# (1dp)

Hence,

The objects rate of acceleration is

#7.91 \ ms^-2# (2dp)

The direction of the acceleration is at an angle of#71.6º#